Summary. 1 Introduction
|
|
- Maude Singleton
- 5 years ago
- Views:
Transcription
1 Exlaining th Vaiation o th Poton Radis in Exints with Monic Hydogn Policao Yōshin Ulianov Changing Rivs by Ocans olicaoy@gail.co Say n xints o oton adis asnt that s onic hydogn, th val obtaind was o cnt blow th xctd standad val, which is not xlaind by qant lctodynaics. This aticl thotically xlains this slts and snts an qation that calclats th oton adis, which coincids with th val obtaind in onic hydogn xints, with a dinc o only 0.07 cnt. Ths slts a basd on Ulianov Sting Thoy (UST), a nw Sting Thoy, which is abl to odl th ost iotant aticls in o nivs as hotons, otons, lctons, ntons, ons and ositons. Th atho blivs that th xint with Monic Hydogn snts a bakthogh in odn hysics, bcas it oints ot laws in th standad odl and ons sac o nw thois that odl th lcton and oton as stings. Th xinc with onic hydogn ay lad to a odl in which th lcton is no long a "sall ball" obiting th ncls and it tns into a twodinsional ban sonding th ncls. Ths, this xint has th otntial to b so iotant, sch as th histoical xinc o th Michlson intot, which akd th nd o th ondanc o th Nwtonian chanics. 1 ntodction This aticl was dvlod basd on slts obtaind in th contxt o Ulianov Sting Thoy [1] (UST), a nw ty o Sting Thoy, which is th otco o a solitay wok od by th atho o abot 0 yas. This wok was initially dvlod by th atho as a hobby, sking th constction o a "ictional nivs", in oth wods, a colt and athatically cohnt nivs (bt not connctd to o own nivs) that can b silatd on a digital cot. Th UST was catd o a w sil ls, sch as th ida o "qadl nivs" oosd by saac Asiov in a scintiic aticl blishd in 1966 []. n this aticl, Asiov snts an innovativ xlanation o th xcss o att in o nivs. n that sa ya o 1966, th Rssian hysicist Andi Sakhaov has also oosd an xlanation o th obl o antiatt "loss" in th cation o o nivs. Sakhaov oosd that a sall ibalanc in th oation and annihilation ocss o att / antiatt wold hav ld to th ondanc o att. Th Sakhaov soltion was widly blicizd and acctd, and it ss that no sios scintist has had lastways noticd th xlanation oosd by Asiov. This ay hav occd bcas saac Asiov had a gat oinnc as a scinc iction wit, and his scintiic aticls (blishd in books and agazins aid at an otsid adinc) had bn sohow "ixd" with his tals o scinc iction. Howv, Asiov's gniality in cating ictional stois was not an idint so that h cold hav gat idas in scinc aas, sch as th ola clov nivs[], which givs bas to th Ulianov Sting Thoy. Th UST odls s a vy sil athatics, bt that is basd on a owl st o idas that s sohow latd to th bass that o o nivs. This obsvation was ad by th atho who, ding th dvlont o th UST, noticd th gnc o a sis o stcts that coos att and ngy aticls that in so ascts a siila to aticls obsvd in o nivs. Moov, th UST gnats odls that allow calclating so vals that a considd hysical constants in standad odl, as th oton adis, hydogn ato adis, on ass, and th lctic chag o th lcton. Ths, by odling th oton at UST it was ossibl to gnat an qation o calclating th oton siz, bt th val obtaind is o cnt blow th standad val. Coincidntally, th obl o obtaining a oton with adis low than th xctd was also 1
2 occing in xints with onic hydogn. Ths xints s ons (aticls with ngativ chag and ass 00 tis gat than that o th lcton) that a lanchd against hydogn atos. n so cass, a on lacs an lcton, oing a onic hydogn ato. Sinc th on is havi, it shold, in incil, allow asing th oton adis with gat cision. Howv, in th slts obtaind with onic hydogn, th adis val asd o th oton was o cnt blow th xctd standad val. nitially, hysicists thoght that th inconsistnt slts coing o so xintal obl, bt at a long and ticlos wok, a ta o hysicists ld by D. Randol Pohl [], blishd in Jly 010 an aticl, in which th slts o th xints with onic hydogn w acctd as t, aising qstions on so oints o th thoy o th qant lctodynaics, on o th "jwls" o th standad odl o odn hysics. Whn th atho bca awa o th wok blishd by D. Pohl's ta, h viid that th val o th oton adis obtaind in th xint with onic hydogn was alost th sa to th thotical val obtaind o th basic odl o th oton dind in th UST. Th atho thn contactd th D. Pohl ta and sbittd th UST qation, which allows calclating th oton adis. D. Pohl conid that th thotical val obtaind in UST qation was alost qal to that obtaind xintally by his ta, bt hasizd that th actal obl wold b to xlain th ason why dint xints w gnating dint slts whn asing th adis o th oton. Th stdy o th xint with onic hydogn in th contxt o UST was a big dal, bcas it concldd so ascts o this thotical odl and also gnats a link with slts o an iotant xint, which is not cntly xlaind by standad odls o hysics. Ulianov Sting Thoy Ulianov Sting Thoy (UST) is a nw ty o sting thoy, in which all aticls o att and ngy a coosd o nctal aticls that ov in sac in nction o a colx ti, coosd o a al at (al ti) and an iaginay at (iaginay ti). Th collas o th iaginay ti tansos ths aticls into cods o stings, which can b viwd as sqncs o sall shs (with diat qal to th Planck distanc), which align in sqnc, lik bads on a ncklac, and wa thslvs in dint os, gnating cvd lins, aas (bans) and also vols. n UST, all stings hav th sa lngth, ths th sting that cooss on hoton is, in so ascts, vy siila to th stings that o a oton o an lcton. Colx Ti in UST On o th ost basic ascts o Ulianov Sting Thoy is th tatnt o ti as a colx vaiabl ( s ) that can b dind by: s t+ i q (1) Wh t snts al ti and q snts th iaginay ti. n UST, th colx ti can b dind on a cylindical sac, in which th dinsion o iaginay ti has a ixd lngth qal to th it o a cicla sction dind in this cylind. L q 1 i q - L Fig 1 Flattnd sntation o th colx ti. Fig 1 shows a lattnd sntation o colx ti, wh L snts th lngth o iaginay ti. Th al ti, in tn, has no liits in this odl, assing a val that xands continosly. 4 Fndantal aticls in th UST odl A oint aticl ( ϕ ) dind in a th-dinsional sac oving in a nction ( F ) o a colx ti, can b gnally odld by: t 1 s 1 t
3 ϕ ( x, y, z) F( t, q) () Considing that this aticl ovs in sac as a nction o iaginay ti, dscibing a non-nll tajctoy, th collas o th iaginay ti will tanso this aticl into a sting, bcas th ositions that th aticl occis in nction o th vaiation o th iaginay ti, will xist all at onc. All aticls odld in th UST ov (in colx ti) at sd o light ( c ). On this way, th sting gnatd by th collas o th iaginay ti will hav a lngth ( L ) givn by th ollowing qation: ig snts an hol with nll chag and ositiv ass, whil th whit cicl snts an hol with nll chag and ngativ ass. Fig - Basic sting odling hoton in UST. Th basic hoton sting shown in Fig was dnoinatd, in UST, as hotonic ing. t has a adis, that is associatd to th wavlngth o th hoton ( λ ), by th ollowing qation: L c L () λ (5) Considing that th aticls which align to o a sting hav non-nll siz, ach aticl can b sntd by a sall sh, o a sall cb that contains this sh. This cb can b dind by th siz o yo hand ( ) which is also qal to th diat o th considd sh. Assing that th od sting is coosd o th nb ( M ) o alignd shs, this val can b calclatd by: c L M (4) Not: Th sall shs oing stings in UST odl a connctd to nctal aticls, calld Ulianov Hols (hols). Ths, a UST sting is coosd o hols sqncs, which can b classiid into six ajo tys, ach containing dint vals o ass and lctic chag. A o colt dscition o hols can b obsvd in nc [1]. 5 Th hoton odld by UST n UST, th hoton is a basic ty o sting which was itsl in a cicla ing, as shown in Fig. n this ig, th d cicls snt hols with nll ass and ngativ lctical chag and th bl cicls snt hols with nll ass and ositiv lctical chags. Th black cicl shown in this Th lngth o th hotonic ing is sally ch sall than th lngth L, which is dind by qation (). This ans that th hoton basic sting is olld in ( N ) ovlad tns. Fo qations () and (5), th nb N o tns o th hotonic ing can b calclatd by th qation: c L (6) N λ n th hoton odl adotd in UST shown in Fig, o ach voltion o th hotonic ing th a only two aticls with ass. On o ths aticls has nitay ositiv ass (att aticl) and th oth has nitay ngativ ass (antiatt aticl). Ths, th total ass in hotons is zo bt, vn so, thos aticls with ass also hav kintic ngy associatd, which can b xssd by th basic qation that lats th ngy ( E) o a ass () oving at a vlocity (v): E v (7) Not: Th UST odl consids that th antiatt has ngativ ass, bt its kintic ngy is still ositiv. Ths, in UST it is ncssay to s a odl nction ov th ass
4 val in all qations that lat th ass (att and antiatt) to ngy. Sinc th a N tns in ach hoton, th ositiv ass o a hoton ( ) is givn by: E h c c L λ λ h L c 6 Poton odl in UST (1) c L N λ (8) Wh is th ass associatd to an hol, givn in kilogas, which can b calclatd basd on th val o L. Th ngativ ass o th hoton ( ) has th n sa val givn by qation (8), bt with oosit sign: n UST, th oton is odld by a sting siila to that which os th hoton, bt only containing aticls (hols) with ositiv ass and ositiv lctical chag, as shown in Fig. c L n λ (9) Ths, in th UST odl, th kintic ngy o th hoton is obtaind by considing that both sts o aticls with ass (att and antiatt) ov (obviosly) at th sd o light: Fig - Basic sting which os th oton. n th cas o th oton, th basic sting shown in Fig is olld in concntic tns, assing th sha o a cicla ban, as shown in Fig 4. E E c c + n c (10) Ths, by alying th qation (8) into qation (10), w obtain: c L E c λ E c L λ (11) n standad odl, th hoton ngy can b calclatd by th ollowing qation: Wh h is Planck's constant. h c E λ (1) Eqaling th ngy in qations (11) and (1), it is ossibl to obtain th ollowing lation: Fig 4 - Basic sting which os th oton in a o alistic sntation. Dsit th act that th basic sting that os th oton was coosing a lat aa, its ovall lngth is still ch sall than th lngth L dind in qation (). Fig 5 - Basic sting which os th oton with all tns sntd. 4
5 Ths, th basic oton sting will also anist itsl in sval tns, which can b god on ach oth, gnating a sntation in cylindical sha, as shown in Fig 5. Howv, th UST sntation o oton shown in Fig 5 is siliid, so that it dos not consid a alistic distibtion o th oton chag distibtion in sac. n a o alistic odl, th cicla aa oing th oton basic sting tnds to aintain th sa cntal axis in sac, assing dint otation angls and itting as th bds o an oang. Fig 6 shows a to viw o basic stings that o th oton, accoding to two distinct sntations. n th 6-a sntation, w hav a siliid sntation o th oton that has th sha o a assiv cylind (which was shown in Fig 5). n th 6-b sntation, th oton sting asss th sha o a solid sh, as shown in Fig 7. (a) (b) Fig 6 - To viw o th cicla aas that o th oton. a) Rsntd in a cylindical sha. b) Rsntd in a shical sha. n od to calclat th oton adis, it is o convnint to consid th siliid sntation shown in Fig 5, instad o sing a shical sntation sntd in Fig 7. Th sag o dint sntation o th aticls in UST, is bst discssd in it 7 o this aticl. Basd on Fig 5 oton sntation, w can ass that it consists o a lag nb o sall shs (hols) alignd in lina lays within th vol o th cylind shown in this ig. n this cas, it is ossibl to associat a cbic vol ( ) o th total sac occid by a sh, and ths th total nb (M) o shs can b dictly calclatd, considing th cylind vol as th ollowing qation: M (14) Sinc UST consids that all aticls a od by stings that hav th sa nb (M) o hols, w can qal th qations (4) and (14): c L c L (15) n addition, in Figs 4 and 5 w can obsv that th oton ass is od by two ovlaing lans. Ths, w can calclat th oton ass ( ) by sing th ollowing qation: Poton ass Fig 7 - Colt sting that os th oton in a o alistic satial sntation. n th odl shown in Fig 7, th oton can b obsvd as a ct sh, within which ositiv chags a distibtd accoding to a nio dnsity. n this odl, th oton ass asss th sha o a sicicl that is instd in th sh "qatoial" sction, sntd in black in Fig 7. Alying qation (16) into qation (15): c L c L c L (16) (17) 5
6 Ths, alying qation (1) into qation (17), w obtain: h c c h c h c (18) Considing th ollowing vals o th sd constants [4]: h x10-4 kg s -1 c s x10-7 kg By alying ths constants into qation (18), th oton adis can b calclatd as: x10-16 (sntd in Fig ), bt it is coosd by ngativ lctical chags, as shown in Fig 8. Fig 8 - Basic sting which os th lcton. n th cas o lcton, th basic sting is also wad in sval coils. n a o accat satial sntation, ths stings volv aond a coon axis and gnat a shical sac as shown in Fig 9. n this ig, only th tns o th lcton basic sting a sntd, ths in actic, th will b illions o tns, coosing a ban that taks th sha o a shical shll. W obsv that th oton adis asd in xints with onic hydogn ( x10-16 ) has a dinc o only 0.07% in lation to th oton adis val, which was calclatd by qation (18). 7 Th xintal obl Th UST odl lads to a oton adis val alost qal to th on that th D. Pohl ta obtaind in th xints with onic hydogn. Bt notnatly it is not ossibl basd only on this nical slt to ai that sohow th oton odl dind in th UST is coct. Th UST shold also b abl to xlain th ason why th aant siz o th oton (asd in both hydogn atos, as in sval xints o lctonic dission) dis so ch o th val obtaind with onic hydogn. Th atho blivs that th UST odl has an answ to this qstion, and it will b sntd in this wok. Bt ist w nd to bily snt th UST odls o th lcton and th on. Fig 9 - Two tys o sntation o th shical shll that os th lcton. Fig 9 snts two os o sin, in which th basic sting o th lcton (shown in Fig 8) can b oganizd in od to coos a shical shll. n th ist cas, th ngativ chags oing th lcton a distibtd on a shical sac, whil its ass is concntatd in a lin on th "qato" o th sh, as shown in Fig 10. Elcton ass 8 Th lcton in UST odl n UST, th lcton is odld by a basic sting, qit siila to th sting that os th oton Fig 10 - Satial sntation o th ban that os th lcton. 6
7 Fig 11, on th oth hand, snts th cas in which lcton chags a also vnly distibtd ov a shical shll, bt in this cas th ass is concntatd at a singl oint on on o th "ols" o th lcton. Poton ass Elcton ass Fig 11 - Anoth satial sntation o th ban that os th lcton. n UST, in addition to th two satial sntations sntd abov, th sting that os th lcton can also wa lik a shical calott, as sntd in Fig 1. This lcton odl is qit intsting bcas it xlains how two lctons that hav oosit sins can join in a sa "obital". n this cas, a hli ato, o xal, which will consist o two ovlaing shical calotts, nitd by its asss and occying a niq sh. Fig 1 - Rsntation o th oton with its ass occying a cylindical aangnt. A gat dtailing o ach satial sntation o lctons and otons considd by UST is byond th sco o this aticl. Howv, it is iotant to not that th conigations o stings that can b sd to xain so basic ascts o ach aticl do not dictly dnd on a alistic satial sntation. This UST asct can b obsvd on th analogy sntd in Fig 14. This ig contains a hotogah o a son in ont o th atwok "Halo" odcd by Anish Kao [5]. Considing siltanosly Figs 6 and 14, w can stablish so siilaitis, and obsv that th satial sntation o th oton is analogos to th agntd iag o an objct (a son) lctd on th ios o Halo. Elcton ass Fig 1 - Elcton ban coosing a shical calott with its ass distibtd in a cicla ing. t is iotant to obsv that at UST, th ost alistic satial oton odl, shown in Fig 7, also has altnativ sntations, as th on shown in Fig 1, in which th oton ass is odld by a cylind aangd in a adial diction, as shown in this ig. Fig 14 - Photo o Halo, an atwok by Anish Kaoo. 7
8 n this analogy, i w want to stdy basic ascts o th objct (o son), it is ch asi to look at it dictly than to dal with its agntd iag. Siilaly, in od to stdy th oton it is asi to consid th siliid sntation shown in Fig 5 than dal with o alistic satial sntations shown in Figs 7 and 1. Ths, a ky oint o th stdy o any aticl in th UST is to obtain its siliid sntation. Fo th cas o th lcton, Fig 15 shows a siliid sntation which is basically a cicla aa with adis qal to (lcton adis) illd by hols with ngativ chag. n this sntation, th lcton ass was god into a ch sall cicla aa with adis qal to (adis o th lcton ass) sntd in black in th ig. Fig 15 - Siliid sntation o th ban that os th lcton. Whn analyzing Fig 15, w can in that th nb (M) o hols oing th ban o th lcton can b calclatd by dividing th aa dind in th d cicl by th aa occid by an hol: M (19) n UST, th total nb o hols o th lcton is qal to th oton s, and ths th qation (14) can b qald to th qation (19): Considing now th aat ρ dind by th lation btwn th oton ass and th lcton ass: ρ Sinc th standad val o ρ is 186,165. (1) A siila lationshi, sntd by th aat σ, can b dind considing th adis o ths two aticls: σ () Noting that in UST, th adis o th lcton is qivalnt to th adis o a hydogn ato (1.06x10-10 ). Alying th standad val o th oton adis (8.768 x10-16 ) in qation () w obtain: σ 10894,16 Siilaly, i w aly th val o th oton adis asd in xints with onic hydogn ( x ) in qation () w hav: σ 15914,66 Accoding to UT th vals o ρ and σ dnd on th lngth o th iaginay ti ( L ). Ths, ths two constants can b latd by on qation, that in th contxt o UT can b dind as ollows: σ 8ρ () (0) And so w can calclat: σ (ρ) 15556,08 (4) 8
9 Not that th val obtaind by qation (4) is.7% abov th val obtaind sing th standad adis o th oton and 0.8% blow th val obtaind sing th oton adis obtaind in xints with onic hydogn. Alying th qation (4) in qation (0): Bing obtaind: 9/ (ρ) (ρ) 5,5619x10-6 Alying th qation (5) in qation (14): Bing obtaind: M ( M (ρ) ) 9 (ρ) M 1,07x10 1 (5) (6) Siilaly alying th qations (5) and (6) in qation (4), th lngth o iaginay ti can b calclatd as: M L c L 6 (ρ) c (ρ) (ρ) c 9 (7) Bing obtaind o th val o th standad oton adis: L 0,008 s Dining th lngth o iaginay ti in nits o Planck ti: L Planck L 5 c h G L x10 40 Planck Th abov val snts th nb o oint aticls that o th stings in th odl UST. Alying qation (7) in qation (1): Bing obtaind: h c L h c (ρ) c h c (ρ) 6,68x10-48 kg 6 (8) Fo Fig 15, w can also calclat th ass o th lcton ( ) thogh th qation: (9) Alying th qations (18) and (1) w can lat th adis containing th ass o th lcton ( ) with th lcton adis ( ), as ollows: ρ ρ (0) ρ Alying th qation (4) in qation (0): (ρ) ρ ρ ρ (1) Eqation (1) indicats that th adis containing th ass o th lcton, shown in Fig 15 as a 9
10 black cicl is actally 6.7 illion tis sall than th adis o th lcton. 9 Th odl o th on in UST obtaind by th nion o siliid UST sntations o th lcton (Fig 15) and oton (Fig 5), as shown in Fig 18. n UST, th on is basically odld as an lcton which shical shll is coosd o sval lays. Ths, th adis o th on tnds to b ch sall than th lcton s, and its ass tnds to b ch high. N w Th on can also b sntd by a basic sting sntd in Fig 16, coosd o ngativ chags and ositiv asss, chaactizd by th adis o th on ( ). ρ Fig 18 - Mban that os th siliid sntation o th on. Fig 16 - Sting that os th basic ing o th on. A o accat satial sntation o th on is shown in Fig 17. n this sntation, w obsv that th on is coosd o a shical shll with a wall thick than th lcton s, bcas it is od by sval lays (sval concntic shical shlls). Not: Th sntation o th ass o th on in a ctangla sha, shown in Fig 18, aas in nction o th ty o distibtion o th considd shs (hols). Fo a sa nb o hols, as shown in Fig 19, th a two basic tys o distibtion coosing a o coact aangnt (Fig 19-a) o o "sacd" (Fig 19-b). Abstacting o th individal shs, ths aangnts can b associatd to th cicla and ctangla aas, which a obsvd in Fig 19. Mon ass ρ (a) (b) Fig 19 - Two tys o aangd shs in a cicla and ctangla aa. Fig 17 - Mban oing th on in a satial sntation. n od to btt odling th on, w st initially obtain its siliid sntation. Th chag distibtion o th on is siila to th lcton s, and so, considing that th ass distibtion in th on is siila to th oton s, th siliid sntation o th on can b Whn analyzing th on siliid odl in Fig 18, w can calclat th nb (M) o hols that os th on, as dind by: M ρ Alying th qation (19) into qation (): () 10
11 5 ρ 4 ρ Alying th qation (5) into qation (): 10 8 ρ ρ 9 7 ρ (ρ) 9 () (4) Likwis, by th on sntation sntd on Fig 18, th on ass ( ) can b calclatd by: N w (5) Wh N is th nb o shical shlls that w o th walls o th on and is th adis o th on ass. n UST odl, th adis o th on ass ( ) can b dictly latd to th adis o th lcton ass ( ). This occs bcas th lcton ass snt on th shical shll is aintaind alost at th sa ootions in ach shical shll that os th on. Ths, th qation o o (5) can b wittn as: Dividing qation (6) by qation (9): N N w N w w (6) (7) Eqation (7) indicats that th lation o th on and lcton asss is ootional to th nb o "lays" o th on. This is qivalnt to say that th cicla aa containing ass that xists in th "ol" o an lcton will also occ at ach lay o th on, bt with a satial distibtion a littl lss coact, which gnats th ltilication acto /. n od to dtin th val o N w can w calclat th nb o tns (o a sa basic sting) that xists in th lcton ( N ) and th nb o tns that th is in th on ( N ): c L N c L N (8) (9) Considing thn that N ings o lctons gnat a ban o nitay thicknss, th total nb o lays in th ban o th on can b calclatd sing th ollowing qation: N w N N (40) Alying th qations (4) and (40) into qation (7): ρ 7 (41) Considing th dalt val o ρ, w can calclat o qation (41) th lation btwn th on ass and th lcton s: 04,09 Knowing that th dalt val o th abov lation is qal to , th dinc btwn ths two vals is only 1.%. 11
12 10 Exlaining th onic hydogn At obsving a sall at 1 o th UST qations that odl th hoton and so atial aticls (lcton, oton and on), it is ossibl to xlain why th otons in onic hydogn chang its adis in lation to th oth standad xints. Fistly, w nd to obsv that all analysis o aticls ad so a in this aticl only consid ach aticl saatly. Ths, o xal, th adis o th oton calclatd by qation (18) snts th val at st, in which this oton dos not intact with oth aticls. This condition is not valid, o xal, o a hydogn ato, bcas as shown in Fig 0, th oxiity o th oosit lctical chags o th oton and lcton gnats attaction ocs (yllow aows in th ig) so that th adis o th oton tnds to incas as th lcton adis tnds to dcas. 0 1 Fig 1 - Placing a on and a oton togth. This occs bcas althogh th odl sntd in Fig 1 is asibl, it dos not snt th hysical conigation obsvd in onic hydogn. Obsving th aticls shown in Figs 0 and 1 in a o alistic sntation, i th oton was th siz o a a, hnc th lcton wold b th siz o a ootball ild, whil th on wold b th siz o a izza Ths, in th UST odl, an lcton "cat" a oton in its intio is a lativly tivial vnt as asy as thowing a ootball in a ild and hit th gass. Now ty th sa "shot" at a tagt that has th siz o a izza. 1 1 t0 t1 Fig 0 - Placing an lcton and a oton togth. n th onic hydogn oation, th lcton will b lacd by a on, lading to th odl shown in Fig 1. Howv, by lacing a oton "insid" a on w obsv a contadiction with th xintal slts, bcas in this condition, in which th chags o th on a clos, th oton adis wold tnd to gow vn o. 1- Fo silicity so additional oints w not addssd, o xal, th qations o th aticls tajctois. t Fig - Foation o onic hydogn. What hans in th cas o onic hydogn is that th on dos not "cat" th oton (insid it), bt only gts in obit aond it, as shown in Fig. n this condition, th on 1
13 chag acts th oton as a whol withot gnating signiicant ocs to xand this adis. Ths, th siz o th oton in th onic hydogn is actically qal to th siz o th oton in a sting condition, whos adis is odld by th qation (18). This xlains th oton adis val obtaind in th xint with onic hydogn, bt it is still issing to xlain th siz o th oton obsvd in a hydogn ato, which will b sntd in sbsqnt sctions o this aticl. 11 Vaiation o th oton ass in atoic ncls A basic asct o th UST odl is that all att and ngy aticls a od by stings that always hav th sa lngth. Ths aticls will ass dint satial conigations, by bing wad in sccssiv tns. n addition, in UST odls th nb o tns is dictly latd to th aticl ass. This asct can b obsvd thogh th analogy sntd in Fig, wh a "al" sting (sntd in d in this ig) is sotd by a st o llys (sntd in bl), kt sttchd by a st o wights (sntd in black) attachd at its bas. n this analogy, th total lngth o th sting dos not chang, bt th lngth L (o ach tn o a basic sting) will tak only a w disct vals in nction o th nb o wights sd. Ths, i it is ncssay to incas th val o L, w st liinat so wights (discad ass) ntil obtain th dsid lngth. Moov, in od to dcas th val o L, w nd to s a lag nb o wights (and llys). lngth, this ilis that its ass st ncssaily dcas. Likwis, i th ocs gnat a dction in th basic sting lngth, th ass shall incas. Fo a oton ovd o an isolatd sitation and lacd into th ncls o a hydogn ato, as shown in Fig 0, th intaction o th oosit chags will cas th oton to incas its adis and, consqntly, will gnat a dction in its ass. This odl can b odd to taditional hysics, bt w obsv that th vaiation o th oton ass that occs as a nction o its adis vaiation ctly xlains th ason why th o colx atos ncls a havi. Dsit th ngativ chags o an lcton attacting all th otons insid th ncls, it is ossibl to wok with a siliid odl, by associating ach lcton to only on oton. Ths, i w cold bild atos by adding lctons and otons (and ntons) on by on, w wold obsv that o lag lctons (o xtnal to th ncls) th ct o attaction on th cosonding oton is sall (bcas th ngativ chags a th away), and hnc th oton xands itsl lss and bcos havi n 5 n 1 n 4 4 n n L Fig - Analogy o a al sting sotd by llys and hangd by th wights. n th analogy o Fig, i th sting is sbjctd to th ocs that gnat an incas in Fig 4 - Bylli ato in th UST odl. Th ith nton was aintd in d to acilitat th visalization. Fig 4, o xal, snts th UST odl o th bylli ato. This ato has o lctons, o otons and iv ntons. n this cas, two lctons a clos to th ncls (obital 1s in th standad odl) and th otons associatd to th will b lag and light. Th aining lctons will hav a adis slightly lag (obital s) and th associatd otons will 1
14 b sall and havi. Ths, th avag wight o otons in a bylli ato tnds to b high than in th hydogn o hli ato. 1 Th siz o th oton in th hydogn ato Considing a hydogn ato, w can calclat th nw adis o th oton insid aking a odiication in qation (18): 1 h c 1 h c ( 0 Wh: adis o a oton in a sting condition; 0 ) (4) adis o "sttchd" oton (d to 1 intaction with th lcton); oton ass vaiation that occs d to its adis vaiation. Accoding to th UST, th val can b stiatd basd on th Fi ngy o th atoic ncls, whos tyical val is 8 MV [6]. Ths, w can consid th val to b qal to this Fi ngy convtd into a ass val: , ,77 10 kg c Using this val in qation (4), w obtain: 8, W can obsv that th oton adis calclatd abov tnds cisly to th oton standad adis (8.768 x ) with an o o only 0.068%. Not: n th UST odl, th oton tns aond its ola axis, and ths it will hav a kintic ngy that dnds both on its ass and its adis and otation sd. Ths, th ass loss obsvd whn a oton cobins with an lcton to o a hydogn ato is consatd by th vaiation in th oton adis and th otation sd. Tho, th total ngy o th syst ains -16 alost constant, bcas th ass "lost" by th oton tns into kintic ngy. 1 Conclsion This aticl shows that th slts obtaind in th xint o onic hydogn a coct and that th oton actally changs siz whn intacting with ons instad o lctons. Th dinc in oton adis vals obtaind o th UST odl and in th xints od by D. Randol Pohl's ta is only 0.07%, a val that cold hadly b coincidntal. n addition, th UST odl is abl to calclat th standad oton adis with a dinc o only 0.068%. Histoically, th lcton was odld on th Boh ato [7] as an ininitsial "sall ball" that concntatd all its ngativ chag and ass, and volvd aond th atoic ncls. This odl gnats a aadig that w call "lcton-sall ball" and has aind valid vn in th ondations o qant chanics, in which th lcton ca to b odld as a wav nction. This occs bcas th lcton wav nctions a associatd to th obitals aond th atoic ncls and a inttd as obability nctions o th satial distibtion o this lcton-sall ball". n th lcton odl oosd in UST, what w s is a ban coosd o a lag nb o ngativ nctal chags (hols), which xist siltanosly, tho gnating a aadig known by th atho as "lcton-ban. Fo th hydogn ato, this ban taks th o o a shical shll coosd o ngativ chags with th lcton ass concntatd in on ol o this sh. Althogh th illstations sntd in this aticl show th lcton as an iobil shical shll, indd o UST, th ban that os th lcton is not static, bt it oscillats and otats aond th ncls. This ilis on a o advancd odl, th gion occid by th lcton aond th atoic ncls cannot b dscibd by a static ban, sch as an idal shical shll. n this cas, th lcton ban st also b dscibd in ts o obability distibtion, which o th lcton in hydogn ato gnats a satial distibtion 14
15 nction siila to th nction dind in qant chanics o th obital S. n actical ts, this ans that th "lctonban odl sd in UST and th wav nctions o qant chanics lad to inal slts qit siila, bt at sciic oints, sch as th xint with onic hydogn, th slts a qit distinct. This occs bcas vn o colt odls, sch as qant lctodynaics, do not os that an lcton will ndgo a oton to a adial oc ild that tnds to xand it. n oth hand, th "lcton-ban odl sd in UST allows not only xlaining th oton adis vaiation, bt also to calclat accatly th vals o th oton adis o th onic hydogn and o th convntional hydogn. Ths, th atho consids that th xint with onic hydogn snts a bonday in odn hysics. Th atho coas this xint to th invtd bidging shown in Fig 5, sinc it conncts th lcton- sall ball odl (which occs whn th on tns aond th oton in th onic hydogn) to th lcton-ban odl dind in UST contxt. Fig 5- vsd Bidg, which conncts China to Hong Kong, coatibilizing th taic on th lt that taks ct in Hong Kong, with th ight taic acticd in China. Th atho blivs that th coct inttation o what is haning with th oton in th onic hydogn xint shold lad to a viw o th aning o wav nctions sd in qant chanics, considing a lag nb o ngativ chags that ally xist siltanosly. This nw aadig o "lcton-ban, bsids xlaining th vaiation o th oton adis, has th otntial to lcidat so odd bhavios, sch as th act that a singl lcton can int "with itsl" in dobl slit xints. Th UST odls sntd in this aticl a voltionay as aning that not only snt th lcton and oton as bans, bt also calclat th nb o nctal aticls that o ach o th (abot 4x10 aticls). Moov, as sntd in this aticl, th UST is also abl to xlain that gavitational and lctoagntic ocs hav siila intnsitis, bt sinc th a ch o aticls with lctic chag (than aticls with ass) coosing th bans, th total ct o lctoagntic ild is ch gat than th total ct o gavitational ild. Th UST odl is also abl to calclat a sis o vals that a considd hysical constants in oth odls, sch as, th hydogn ato adis (adis o th shical ban that os th lcton) and th on ass. t is iotant to hasiz that th UST odls sntd in this aticl snt only a sall at o th wok odcd by th atho, which is st in a boad sco nad Ulyanov Thoy (UT), also inclding: A cosological odl calld Sall Bang Thoy [8], in which th nivs is catd in a "slow" way, bcas initially th is only th iaginay ti. A sntation o non-eclidan sacs, nad Ulyanov Sh Ntwok (USN) [9], which allows ddcing slts qivalnt to th Einstin's gnal lativity, as wll as Nwton's gavitation law. Ths, althogh th odls dind in UT a still incolt and ossibly containing any os and inconsistncis, thy hav so basic idas qit innovativ, sch as th s o iaginay ti, th aadig "lcton-ban and th saation o aticls with lctic chags and asss in th ban oation, which has th otntial to voltioniz any aas o odn hysics. Th atho wold lik to invit on-indd hysicists to wok togth in dvloing and 15
16 tsting UST odls sntd in this aticl, as wll as in nw odls dind within th Ulianov Thoy. Rncs: [1] Policao Y. Ulianov: Ulianov Sting Thoy - A nw sntation o ndantal aticls. Agst [] saac Asiov: ' Looking ov a Fo- La Clov. Fist Pblishd n: Th Magazin o Fantasy and Scinc Fiction, S Collctions: Scinc, Nbs, and, 1968; Asiov on Scinc Jly-1989, blish Doblday, ASN: [] Randol Pohl, Aldo Antognini, Fançois Nz, Fnando D. Aao, Fançois Biabn, João M. R. Cadoso, Danil S. Covita, Andas Dax, Satish Dhawan, Lis M. P. Fnands, Adol Gisn, Thoas Ga, Thodo W. Hänsch, Pal ndlicato, Lcil Jlin, Chng-Yang Kao, Pal Knowls, Eic-Olivi L Bigot, Yi-Wi Li, José A. M. Los, Livia Ldhova, Cistina M. B. Montio, Fançois Mlhas, Tobias Nbl, Pal Rabinowitz, Joaqi M. F. dos Santos, Lkas A. Schall, Kastn Schhann, Cathin Schwob, David Taqq, João F. C. A. Vloso & Fanz Kottann: Th siz o th oton. n: Nat; 466, 1-16; 8 Jly 010. [4] NST: CODATA ntnationally condd vals o th ndantal hysical constants. htt://hysics.nist.gov/c/constants/indx.htl [5] Anish Kaoo: Halo. 006; Lisson Gally. htt:// [6] Fi ngy, o Wikidia, th ncyclodia htt://n.wikidia.og/wiki/fi_ngy [7] Boh odl, o Wikidia, th ncyclodia htt://n.wikidia.og/wiki/boh_odl [8] Policao Y. Ulianov: Sall Bang Ciando nivso a ati do nada d [9] Policao Y. Ulianov: Ulianov Sh Ntwok - A Digital Modl o Rsntation o Non-Eclidan Sacs, Abot th Atho: Policao Yōshin Ulianov is an lctical ngin with Masts in lctonic sckl hologahy and Doctoat dg in atiicial intllignc aa. H stdis thotical hysics as a hobby and thoghot 0 yas o sach, h boght togth a sis o idas h considd intsting, and dvlod a odl calld Ulianov Thoy, which odls a ictitios hysical nivs o a w basic concts dind intitivly. Contacts with th atho can b ad by ail: olicaoy@gail.co Thanks and Congatlations Th atho wold lik to congatlat D. Randol Pohl and his sta o th igoos wok don in th onic hydogn xints. Ctainly, this is a histoical xinc that will nt into th annals o odn hysics. Th atho thanks Solção Snova Sta Ta ( o all sot and svics gading th tanslation o this a o Potgs to English. This aticl is availabl at: 16
Mon. Tues. Wed. Lab Fri Electric and Rest Energy
Mon. Tus. Wd. Lab Fi. 6.4-.7 lctic and Rst ngy 7.-.4 Macoscoic ngy Quiz 6 L6 Wok and ngy 7.5-.9 ngy Tansf R 6. P6, HW6: P s 58, 59, 9, 99(a-c), 05(a-c) R 7.a bing lato, sathon, ad, lato R 7.b v. i xal
More informationUGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.
UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial
More informationRadiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom
14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Radiation Equilibiu, Intia onts, and th Nuclus Radius in th Elcton-Poton Ato H. Vic Dannon vic@gaug-institut.og Novb, 13 Rvisd July, 14 Abstact
More informationGRAVITATION 4) R. max. 2 ..(1) ...(2)
GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body
More informationII.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD
II.3. DETEMINTION OF THE ELETON SPEIFI HGE Y MENS OF THE MGNETON METHOD. Wok pupos Th wok pupos is to dtin th atio btwn th absolut alu of th lcton chag and its ass, /, using a dic calld agnton. In this
More information6.Optical and electronic properties of Low
6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a
More informationMon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9
Fi. on. Tus. 6. Fild of a agntid Ojct 6.3, 6.4 uxiliay Fild & Lina dia HW9 Dipol t fo a loop Osvation location x y agntic Dipol ont Ia... ) ( 4 o I I... ) ( 4 I o... sin 4 I o Sa diction as cunt B 3 3
More informationThe local orthonormal basis set (r,θ,φ) is related to the Cartesian system by:
TIS in Sica Cooinats As not in t ast ct, an of t otntias tat w wi a wit a cnta otntias, aning tat t a jst fnctions of t istanc btwn a atic an so oint of oigin. In tis cas tn, (,, z as a t Coob otntia an
More informationPHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationPHYS 272H Spring 2011 FINAL FORM A. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS. Ghiocel Groza*, S. M. Ali Khan** 1. Introduction
ADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS Ghiocl Goza*, S. M. Ali Khan** Abstact Th additiv intgal functions with th cofficints in a comlt non-achimdan algbaically closd fild of chaactistic 0 a studid.
More informationHydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals
Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas
More informationExtinction Ratio and Power Penalty
Application Not: HFAN-.. Rv.; 4/8 Extinction Ratio and ow nalty AVALABLE Backgound Extinction atio is an impotant paamt includd in th spcifications of most fib-optic tanscivs. h pupos of this application
More informationShape parameterization
Shap paatization λ ( θ, φ) α ( θ ) λµ λµ, φ λ µ λ axially sytic quaupol axially sytic octupol λ α, α ± α ± λ α, α ±,, α, α ±, Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7 Octupol collctivity coupling
More information5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS
5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870
More informationSolid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch
Solid stat physics Lctu 3: chmical bonding Pof. D. U. Pitsch Elcton chag dnsity distibution fom -ay diffaction data F kp ik dk h k l i Fi H p H; H hkl V a h k l Elctonic chag dnsity of silicon Valnc chag
More information8 - GRAVITATION Page 1
8 GAVITATION Pag 1 Intoduction Ptolmy, in scond cntuy, gav gocntic thoy of plantay motion in which th Eath is considd stationay at th cnt of th univs and all th stas and th plants including th Sun volving
More informationKeywords: Auxiliary variable, Bias, Exponential estimator, Mean Squared Error, Precision.
IN: 39-5967 IO 9:8 Ctifid Intnational Jounal of Engining cinc and Innovativ Tchnolog (IJEIT) Volum 4, Issu 3, Ma 5 Imovd Exonntial Ratio Poduct T Estimato fo finit Poulation Man Ran Vija Kuma ingh and
More informationShor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm
Motivation Sho s Algoith It appas that th univs in which w liv is govnd by quantu chanics Quantu infoation thoy givs us a nw avnu to study & tst quantu chanics Why do w want to build a quantu coput? Pt
More informationCollege Prep Physics I Multiple Choice Practice Final #2 Solutions Northville High School Mr. Palmer, Physics Teacher. Name: Hour: Score: /zero
Collg Pp Phsics Multipl Choic Pactic inal # Solutions Nothvill High School M. Palm, Phsics Tach Nam: Hou: Sco: /zo You inal Exam will hav 40 multipl choic qustions woth 5 points ach.. How is cunt actd
More informationLecture 17. Physics Department Yarmouk University Irbid Jordan. Chapter V: Scattering Theory - Application. This Chapter:
Lctu 17 Physics Dpatnt Yaouk Univsity 1163 Ibid Jodan Phys. 441: Nucla Physics 1 Chapt V: Scatting Thoy - Application D. Nidal Eshaidat http://ctaps.yu.du.jo/physics/couss/phys641/lc5-1 This Chapt: 1-
More informationCHAPTER 5 CIRCULAR MOTION
CHAPTER 5 CIRCULAR MOTION and GRAVITATION 5.1 CENTRIPETAL FORCE It is known that if a paticl mos with constant spd in a cicula path of adius, it acquis a cntiptal acclation du to th chang in th diction
More informationChapter 1 The Dawn of Quantum Theory
Chapt 1 Th Dawn of Quantum Thoy * By th Lat 18 s - Chmists had -- gnatd a mthod fo dtmining atomic masss -- gnatd th piodic tabl basd on mpiical obsvations -- solvd th stuctu of bnzn -- lucidatd th fundamntals
More informationLecture 3.2: Cosets. Matthew Macauley. Department of Mathematical Sciences Clemson University
Lctu 3.2: Costs Matthw Macauly Dpatmnt o Mathmatical Scincs Clmson Univsity http://www.math.clmson.du/~macaul/ Math 4120, Modn Algba M. Macauly (Clmson) Lctu 3.2: Costs Math 4120, Modn Algba 1 / 11 Ovviw
More informationCollisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center
Collisionlss Hall-MHD Modling Na a Magntic Null D. J. Stoi J. J. Ramos MIT Plasma Scinc and Fusion Cnt Collisionlss Magntic Rconnction Magntic connction fs to changs in th stuctu of magntic filds, bought
More informationbe two non-empty sets. Then S is called a semigroup if it satisfies the conditions
UZZY SOT GMM EGU SEMIGOUPS V. Chinndi* & K. lmozhi** * ssocit Pofsso Dtmnt of Mthmtics nnmli Univsity nnmling Tmilnd ** Dtmnt of Mthmtics nnmli Univsity nnmling Tmilnd bstct: In this w hv discssd bot th
More informationSTATISTICAL MECHANICS OF DIATOMIC GASES
Pof. D. I. ass Phys54 7 -Ma-8 Diatomic_Gas (Ashly H. Cat chapt 5) SAISICAL MECHAICS OF DIAOMIC GASES - Fo monatomic gas whos molculs hav th dgs of fdom of tanslatoy motion th intnal u 3 ngy and th spcific
More informationChapter 4. QUANTIZATION IN FIVE DIMENSIONS
Chat QUANTIZATION IN FIVE DIMENSIONS Th cding dvlomnt ovids a tmndous walth o mathmatical abstactions Howv th sms within it no adily aant mthod o intting th nw ilds I th aas to b no hysical ntity which
More informationSUPPLEMENTARY INFORMATION
SUPPLMNTARY INFORMATION. Dtmin th gat inducd bgap cai concntation. Th fild inducd bgap cai concntation in bilay gaphn a indpndntly vaid by contolling th both th top bottom displacmnt lctical filds D t
More information(, ) which is a positively sloping curve showing (Y,r) for which the money market is in equilibrium. The P = (1.4)
ots lctu Th IS/LM modl fo an opn conomy is basd on a fixd pic lvl (vy sticky pics) and consists of a goods makt and a mony makt. Th goods makt is Y C+ I + G+ X εq (.) E SEK wh ε = is th al xchang at, E
More informationE F. and H v. or A r and F r are dual of each other.
A Duality Thom: Consid th following quations as an xampl = A = F μ ε H A E A = jωa j ωμε A + β A = μ J μ A x y, z = J, y, z 4π E F ( A = jω F j ( F j β H F ωμε F + β F = ε M jβ ε F x, y, z = M, y, z 4π
More informationMOS transistors (in subthreshold)
MOS tanito (in ubthhold) Hitoy o th Tanito Th tm tanito i a gnic nam o a olid-tat dvic with 3 o mo tminal. Th ild-ct tanito tuctu wa it dcibd in a patnt by J. Lilinld in th 193! t took about 4 ya bo MOS
More informationElectromagnetic Schrödinger Equation of the Deuteron 2 H (Heavy Hydrogen)
Wold Jounal of Nucla Scinc and Tchnology, 14, 4, 8-6 Publishd Onlin Octob 14 in SciRs. htt://www.sci.og/jounal/wjnst htt://dx.doi.og/1.46/wjnst.14.449 Elctomagntic Schöding Equation of th Duton H (Havy
More informationCDS 110b: Lecture 8-1 Robust Stability
DS 0b: Lct 8- Robst Stabilit Richad M. Ma 3 Fba 006 Goals: Dscib mthods fo psnting nmodld dnamics Div conditions fo obst stabilit Rading: DFT, Sctions 4.-4.3 3 Fb 06 R. M. Ma, altch Gam lan: Robst fomanc
More informationGRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6
GVITTION 1. Two satllits and o ound a plant P in cicula obits havin adii 4 and spctivly. If th spd of th satllit is V, th spd of th satllit will b 1 V 6 V 4V V. Th scap vlocity on th sufac of th ath is
More informationElasticity 1. 10th April c 2003, Michael Marder
Elasticity 0th Apil 003 c 003, Michal Mad Gnal Thoy of Lina Elasticity Bfo dfomation Aft dfomation Many ways to div lasticity. Cold div fom thoy of atoms and thi intactions. Howv, this appoach is not histoically
More information( ) 4. Jones Matrix Method 4.1 Jones Matrix Formulation A retardation plate with azimuth angle y. V û ë y û. év ù év ù év. ë y û.
4. Jons Mati Mthod 4. Jons Mati Foulation A tadation plat with aziuth angl Yh; 4- Linal polaizd input light é = ë û Dcoposd into th slow and ast noal ods és é cos sin é = sin cos ë- û ë û R ( ), otation
More informationPhysics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM
Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic
More informationThe tight-binding method
Th tight-idig thod Wa ottial aoach: tat lcto a a ga of aly f coductio lcto. ow aout iulato? ow aout d-lcto? d Tight-idig thod: gad a olid a a collctio of wa itactig utal ato. Ovla of atoic wav fuctio i
More informationToday s topic 2 = Setting up the Hydrogen Atom problem. Schematic of Hydrogen Atom
Today s topic Sttig up th Hydog Ato pobl Hydog ato pobl & Agula Motu Objctiv: to solv Schödig quatio. st Stp: to dfi th pottial fuctio Schatic of Hydog Ato Coulob s aw - Z 4ε 4ε fo H ato Nuclus Z What
More informationFinite Element Analysis of Adhesive Steel Bar in Concrete under Tensile Load
4th Intnational Confnc on Sstainabl Engy and Envionmntal Engining (ICSEEE 2015) Finit Elmnt Analysis of Adhsiv Stl Ba in Conct nd Tnsil Load Jianong Zhang1,a, Ribin Sh2,b and Zixiang Zhao3,c 1,2,3 Tongji
More informationCOMPSCI 230 Discrete Math Trees March 21, / 22
COMPSCI 230 Dict Math Mach 21, 2017 COMPSCI 230 Dict Math Mach 21, 2017 1 / 22 Ovviw 1 A Simpl Splling Chck Nomnclatu 2 aval Od Dpth-it aval Od Badth-it aval Od COMPSCI 230 Dict Math Mach 21, 2017 2 /
More informationHomework 1: Solutions
Howo : Solutos No-a Fals supposto tst but passs scal tst lthouh -f th ta as slowss [S /V] vs t th appaac of laty alty th path alo whch slowss s to b tat to obta tavl ts ps o th ol paat S o V as a cosquc
More information1 Input-Output Stability
Inut-Outut Stability Inut-outut stability analysis allows us to analyz th stability of a givn syst without knowing th intrnal stat x of th syst. Bfor going forward, w hav to introduc so inut-outut athatical
More informationMidterm Exam. CS/ECE 181B Intro to Computer Vision. February 13, :30-4:45pm
Nam: Midtm am CS/C 8B Into to Comput Vision Fbua, 7 :-4:45pm las spa ouslvs to th dg possibl so that studnts a vnl distibutd thoughout th oom. his is a losd-boo tst. h a also a fw pags of quations, t.
More informationThe angle between L and the z-axis is found from
Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt
More informationFourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation
Pof. D. I. Nass Phys57 (T-3) Sptmb 8, 03 Foui_Tansf_phys57_T3 Foui tansfoms (Chapt 5) Foui intgals a gnalizations of Foui sis. Th sis psntation a0 nπx nπx f ( x) = + [ an cos + bn sin ] n = of a function
More informationn gativ b ias to phap s 5 Q mou ntd ac oss a 50 Q co-a xial l, i t whn bias no t back-bia s d, so t hat p ow fl ow wi ll not b p ositiv. Th u s, if si
DIOD E AND ITS APPLI AT C I O N: T h diod is a p-t p, y intin s ic, n-typ diod consis ting of a naow lay of p- typ smiconducto and a naow lay of n-typ smiconducto, wi th a thick gion of intins ic o b twn
More informationOn Jackson's Theorem
It. J. Cotm. Math. Scics, Vol. 7, 0, o. 4, 49 54 O Jackso's Thom Ema Sami Bhaya Datmt o Mathmatics, Collg o Educatio Babylo Uivsity, Babil, Iaq mabhaya@yahoo.com Abstact W ov that o a uctio W [, ], 0
More informationPartial Fraction Expansion
Paial Facion Expanion Whn ying o find h inv Laplac anfom o inv z anfom i i hlpfl o b abl o bak a complicad aio of wo polynomial ino fom ha a on h Laplac Tanfom o z anfom abl. W will illa h ing Laplac anfom.
More informationHow to represent a joint, or a marginal distribution?
School o Cou Scinc obabilisic Gahical ols Aoia Innc on Calo hos ic ing Lcu 8 Novb 9 2009 Raing ic ing @ CU 2005-2009 How o sn a join o a aginal isibuion? Clos-o snaion.g. Sal-bas snaion ic ing @ CU 2005-2009
More informationDiffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of
More informationMid Year Examination F.4 Mathematics Module 1 (Calculus & Statistics) Suggested Solutions
Mid Ya Eamination 3 F. Matmatics Modul (Calculus & Statistics) Suggstd Solutions Ma pp-: 3 maks - Ma pp- fo ac qustion: mak. - Sam typ of pp- would not b countd twic fom wol pap. - In any cas, no pp maks
More informationModule 6: Two Dimensional Problems in Polar Coordinate System
Modl6/Lon Modl 6: Two Dimnional Poblm in Pola Coodinat Stm 6 INTRODUCTION I n an laticit poblm th pop choic o th coodinat tm i tml impotant c thi choic tablih th complit o th mathmatical pion mplod to
More informationGMm. 10a-0. Satellite Motion. GMm U (r) - U (r ) how high does it go? Escape velocity. Kepler s 2nd Law ::= Areas Angular Mom. Conservation!!!!
F Satllt Moton 10a-0 U () - U ( ) 0 f ow g dos t go? scap locty Kpl s nd Law ::= Aas Angula Mo. Consaton!!!! Nwton s Unsal Law of Gaty 10a-1 M F F 1) F acts along t ln connctng t cnts of objcts Cntal Foc
More informationLoss factor for a clamped edge circular plate subjected to an eccentric loading
ndian ounal of Engining & Matials Scincs Vol., Apil 4, pp. 79-84 Loss facto fo a clapd dg cicula plat subjctd to an ccntic loading M K Gupta a & S P Niga b a Mchanical Engining Dpatnt, National nstitut
More informationThe theory of electromagnetic field motion. 6. Electron
Th thoy of lctomagntic fild motion. 6. Elcton L.N. Voytshovich Th aticl shows that in a otating fam of fnc th magntic dipol has an lctic chag with th valu dpnding on th dipol magntic momnt and otational
More informationVaiatin f. A ydn balln lasd n t n ) Clibs u wit an acclatin f 6x.8s - ) Falls dwn wit an acclatin f.8x6s - ) Falls wit acclatin f.8 s - ) Falls wit an acclatin f.8 6 s-. T wit f an bjct in t cal in, sa
More informationMulti-linear Systems and Invariant Theory. in the Context of Computer Vision and Graphics. Class 5: Self Calibration. CS329 Stanford University
Mlti-linar Systms and Invariant hory in th ontt of omtr Vision and Grahics lass 5: Slf alibration S39 Stanford Univrsity Amnon Shasha lass 5 Matrial W Will ovr oday h basic qations and conting argmnts
More informationNEWTON S THEORY OF GRAVITY
NEWTON S THEOY OF GAVITY 3 Concptual Qustions 3.. Nwton s thid law tlls us that th focs a qual. Thy a also claly qual whn Nwton s law of gavity is xamind: F / = Gm m has th sam valu whth m = Eath and m
More informationDiffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of
More informationand integrated over all, the result is f ( 0) ] //Fourier transform ] //inverse Fourier transform
NANO 70-Nots Chapt -Diactd bams Dlta uctio W d som mathmatical tools to dvlop a physical thoy o lcto diactio. Idal cystals a iiit this, so th will b som iiitis lii about. Usually, th iiit quatity oly ists
More informationCalculations and Interpretations of the Different Planck Units
www.ragtc.co/hysiq/ Calclations and Intrrtations of th Diffrnt Planck Units Clad Mrcir ng., Octobr 1 th 14 Rv. Octobr 17 th 15 clad.rcir@gctda.co Planck nits ar art of a nit syst calld "natral". Th nas
More informationPhysics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas
Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain
More informationA 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.
1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with
More informationCHAPTER 5 CIRCULAR MOTION AND GRAVITATION
84 CHAPTER 5 CIRCULAR MOTION AND GRAVITATION CHAPTER 5 CIRCULAR MOTION AND GRAVITATION 85 In th pious chapt w discussd Nwton's laws of motion and its application in simpl dynamics poblms. In this chapt
More informationGet Solution of These Packages & Learn by Video Tutorials on GRAVITATION
FEE Download Study Packag fom wbsit: www.tkoclasss.com & www.mathsbysuhag.com Gt Solution of Ths Packags & an by Vido Tutoials on www.mathsbysuhag.com. INTODUCTION Th motion of clstial bodis such as th
More informationa 1and x is any real number.
Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars
More information(( )( )) = = S p S p = S p p m ( )
36 Chapt 3. Rnoalization Toolit Poof of th oiginal Wad idntity o w nd O p Σ i β = idβ γ is p γ d p p π π π p p S p = id i d = id i S p S p d π β γ γ γ i β i β β γ γ β γ γ γ p = id is p is p d = Λ p, p.
More informationCS 491 G Combinatorial Optimization
CS 49 G Cobinatorial Optiization Lctur Nots Junhui Jia. Maiu Flow Probls Now lt us iscuss or tails on aiu low probls. Thor. A asibl low is aiu i an only i thr is no -augnting path. Proo: Lt P = A asibl
More informationFree carriers in materials
Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting
More informationFree vibration of a magneto-electro-elastic toroidal shell
icccb Nottingha Unisity Pss Pocdings of th Intnational onfnc on opting in iil and ilding ngining W izani (dito) F ibation of a agnto-lcto-lastic tooidal shll. Rdkop patnt of Mchanical ngining, Unisity
More informationCDS 101/110: Lecture 7.1 Loop Analysis of Feedback Systems
CDS 11/11: Lctu 7.1 Loop Analysis of Fdback Systms Novmb 7 216 Goals: Intoduc concpt of loop analysis Show how to comput closd loop stability fom opn loop poptis Dscib th Nyquist stability cition fo stability
More informationPhysics 240: Worksheet 15 Name
Physics 40: Woksht 15 Nam Each of ths poblms inol physics in an acclatd fam of fnc Althouh you mind wants to ty to foc you to wok ths poblms insid th acclatd fnc fam (i.. th so-calld "won way" by som popl),
More informationWhile flying from hot to cold, or high to low, watch out below!
STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud STANDARD ATMOSHERE indicatd altitud actual altitud STANDARD ATMOSHERE Wil flying fom ot to cold,
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble
Quantum Statistics fo Idal Gas and Black Body Radiation Physics 436 Lctu #0 Th Canonical Ensmbl Ei Q Q N V p i 1 Q E i i Bos-Einstin Statistics Paticls with intg valu of spin... qi... q j...... q j...
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationSection 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
More informationThe Australian Society for Operations Research
h Asalian Sociy fo Opaions sach www.aso.og.a ASO Bllin Vol 33 ss 4 Pags 4-48 A Coninos viw nvnoy Mol fo Dioaing s wih Sochasic Dan an Pic Discon on Backos Manisha Pal an Sjan Chana Dpan of Saisics Univsiy
More informationSchool of Electrical Engineering. Lecture 2: Wire Antennas
School of lctical ngining Lctu : Wi Antnnas Wi antnna It is an antnna which mak us of mtallic wis to poduc a adiation. KT School of lctical ngining www..kth.s Dipol λ/ Th most common adiato: λ Dipol 3λ/
More information5-9 THE FIELD CONCEPT. Answers to the Conceptual Questions. Chapter 5 Gravity 63
Chapt 5 Gavity 5-9 THE FIELD CONCEPT Goals Intoduc th notion of a fild. (Pobl Solvin) Calculat th Sun's avitational fild at Eath's location. Contnt Th psnc of a ass odifis spac. A valu can b assind to
More informationEuropean and American options with a single payment of dividends. (About formula Roll, Geske & Whaley) Mark Ioffe. Abstract
866 Uni Naions Plaza i 566 Nw Yo NY 7 Phon: + 3 355 Fa: + 4 668 info@gach.com www.gach.com Eoan an Amican oions wih a singl amn of ivins Abo fomla Roll Gs & Whal Ma Ioff Absac Th aicl ovis a ivaion of
More informationKinetics. Central Force Motion & Space Mechanics
Kintics Cntal Foc Motion & Spac Mcanics Outlin Cntal Foc Motion Obital Mcanics Exampls Cntal-Foc Motion If a paticl tavls un t influnc of a foc tat as a lin of action ict towas a fix point, tn t motion
More informationDual Nature of Matter and Radiation
Higr Ordr Tinking Skill Qustions Dual Natur of Mattr and Radiation 1. Two bas on of rd ligt and otr of blu ligt of t sa intnsity ar incidnt on a tallic surfac to it otolctrons wic on of t two bas its lctrons
More informationCurrent Status of Orbit Determination methods in PMO
unt ttus of Obit Dtintion thods in PMO Dong Wi, hngyin ZHO, Xin Wng Pu Mountin Obsvtoy, HINEE DEMY OF IENE bstct tit obit dtintion OD thods hv vovd ot ov th st 5 ys in Pu Mountin Obsvtoy. This tic ovids
More informationDIELECTRICS MICROSCOPIC VIEW
HYS22 M_ DILCTRICS MICROSCOIC VIW DILCTRIC MATRIALS Th tm dilctic coms fom th Gk dia lctic, wh dia mans though, thus dilctic matials a thos in which a stady lctic fild can st up without causing an appcial
More informationELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION
. l & a s s Vo Flds o as l axwll a l sla () l Fld () l olasao () a Flx s () a Fld () a do () ad è s ( ). F wo Sala Flds s b dd l a s ( ) ad oool a s ( ) a oal o 4 qaos 3 aabls - w o Lal osas - oz abo Lal-Sd
More informationIn the name of Allah Proton Electromagnetic Form Factors
I th a of Allah Poto Elctoagtc o actos By : Maj Hazav Pof A.A.Rajab Shahoo Uvsty of Tchology Atoc o acto: W cos th tactos of lcto bas wth atos assu to b th gou stats. Th ct lcto ay gt scatt lastcally wth
More information4.4 Linear Dielectrics F
4.4 Lina Dilctics F stal F stal θ magntic dipol imag dipol supconducto 4.4.1 Suscptiility, mitivility, Dilctic Constant I is not too stong, th polaization is popotional to th ild. χ (sinc D, D is lctic
More informationProton/Electron mass ratio and gravitational constant due to special relativity
Proton/Elctron ass ratio and gravitational constant du to scial rlativity Prston Guynn Guynn Enginring, 1776 hritag Cntr Driv, Suit 04 Wak Forst, North Carolina, Unitd Stats 7587 guynnnginring@gail.co
More informationEstimation of a Random Variable
Estimation of a andom Vaiabl Obsv and stimat. ˆ is an stimat of. ζ : outcom Estimation ul ˆ Sampl Spac Eampl: : Pson s Hight, : Wight. : Ailin Company s Stock Pic, : Cud Oil Pic. Cost of Estimation Eo
More informationCDS 101: Lecture 7.1 Loop Analysis of Feedback Systems
CDS : Lct 7. Loop Analsis of Fback Sstms Richa M. Ma Goals: Show how to compt clos loop stabilit fom opn loop poptis Dscib th Nqist stabilit cition fo stabilit of fback sstms Dfin gain an phas magin an
More informationLossy Transmission Lines. EELE 461/561 Digital System Design. Module #7 Lossy Lines. Lossy Transmission Lines. Lossy Transmission Lines
Topics EEE 46/56 Digital Systm Dsign. Skin Ect. Dilctic oss Modul #7 ossy ins ossy ins - Whn w divd Tlgaphs Equations, w mad an assumption that th was no loss in th quivalnt cicuit modl i.., =, = - This
More informationInternational Journal of Industrial Engineering Computations
Intnational Jounal of Industial Engining Computations 5 (4 65 74 Contnts lists availabl at GowingScinc Intnational Jounal of Industial Engining Computations hompag: www.gowingscinc.com/ijic A nw modl fo
More informationExtensive Form Games with Incomplete Information. Microeconomics II Signaling. Signaling Examples. Signaling Games
Extnsiv Fom Gams ith Incomplt Inomation Micoconomics II Signaling vnt Koçksn Koç Univsity o impotant classs o xtnsiv o gams ith incomplt inomation Signaling Scning oth a to play gams ith to stags On play
More informationMassachusetts Institute of Technology Department of Mechanical Engineering
Massachustts Institut of Tchnolog Dpartmnt of Mchanical Enginring. Introduction to Robotics Mid-Trm Eamination Novmbr, 005 :0 pm 4:0 pm Clos-Book. Two shts of nots ar allowd. Show how ou arrivd at our
More informationIntroduction - the economics of incomplete information
Introdction - th conomics of incomplt information Backgrond: Noclassical thory of labor spply: No nmploymnt, individals ithr mployd or nonparticipants. Altrnativs: Job sarch Workrs hav incomplt info on
More information217Plus TM Integrated Circuit Failure Rate Models
T h I AC 27Plu s T M i n t g at d c i c u i t a n d i n d u c to Fa i lu at M o d l s David Nicholls, IAC (Quantion Solutions Incoatd) In a pvious issu o th IAC Jounal [nc ], w povidd a highlvl intoduction
More informationAn Elementary Approach to a Model Problem of Lagerstrom
An Elmntay Appoach to a Modl Poblm of Lagstom S. P. Hastings and J. B. McLod Mach 7, 8 Abstact Th quation studid is u + n u + u u = ; with bounday conditions u () = ; u () =. This modl quation has bn studid
More informationWho is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities
Who i thi Gt Tm? Exi Sh th foowing i of infomtion bot of with o tb o tm mt. Yo o not hv to wit n of it own. Yo wi b givn on 5 mint to omih thi tk. Stngt Gift/Fin Niknm Homtown Bt Th Hobb Tv Dtintion Robt
More information