Diode-pump. Introduction into mathematics needed for calculus of the diodepump. 1. Introduction

Size: px

Start display at page:

Download "Diode-pump. Introduction into mathematics needed for calculus of the diodepump. 1. Introduction"

Rosa Marcia Todd
5 years ago
Views:

1 Dod-m Inrodon no mhms ndd for lls of h dodm. Inrodon Th dod-m s rndd n nsgnfn-sml lron r, whh only onsss of 5 omonns, h oml dsron, wh rlly s n ll dls, s long sory. I go g mnng n h 96 s n h rdon-hyss, whr rdov rdon, omng s rls no Ggr-onr, sng hr lron mrng-lss, whh old sd, mong ohrs, o msr hknss of mrl, s nnsy of hrogh-omng rdon ws, d o h rors of nrng rdon, n onnl fnon of h hknss. ogrhmzng wh h volg-rrn-hrrs of dods mld hgh mrr-dndn nd lds whr md for mrr-slsng, rolms wr gr nd h dod-m hd no mrr-dndn. Th dod-m works smlr s wr- or r-m, mng mdm no nk, whh hs hol h oom, whr h mdm s rnnng o gn. Th fsr yo m, h hghr h fllng-lvl n h nk. Th oh dods of h dod-m work smlr s h vlvs of n r-m, hy r only rvos n on dron. Th rl ld nd msrmn of h dod-m s rors dlvrs sffn vls for h ndd frny-rsons-fnon n dndn of h hosn omonns n ordr o g ror dmnsonng. B how n ndrsood mhmlly nd go lld sfons wh omzng lnryrrors nd n gvn nformon o h msrmn-rror? Er md for h gnnrs, ll hory srs, from fr off from h mr, wh h dr on nd how hr roos n fond, Dodm - Pg of -

2 s n h dr on s h orgn, from whr mgnry nmrs om no h ons of lron rs srvng hr s symols for h hrrs, hysl rors of lron omonns. Bs h dr on s h roo of h dffrnl-on of h lr osllon-r nd h dr on hs osonlly, dndng on h sl vls of hr offns, mgnry nmrs s roos, whh or hn n h onns of h onnl-fnons of h dffrnl-on, wh gds s o h rod osllons. And ll hs s r don only o shd lgh on h noon of mdn, whh s r sd o show h rnl of onvrson from rl-r o n vln-r, n ordr o roof, h h vln-r s jsfl o sd for ll knds of rod nd rod sgnls. Bs h vln-r s nssry o mk ll formls smlr. And h s fnlly h omld r-ondon for srng o s h lls-ons for h dodm, whh s shown n h n onron. Th only fnon, whh n srv s solon of h dffrnl on s h onnl fnon, s fr dffrnon rmns nd flls o of h on o mk ossl, h h sm of h on n g zro, whl h dffrnon-offns (. k ) =.k. k, (. k ) =.k. k. form dr on. B s, h solon of dffrnl on s dr on, h roos r osonlly mgnry nmrs. If yo rlly ndrsnd, wh hns ly wh h hrg, f n srs onnd ondnsrs r lodd omnd, yo hv go h rondon for formng n vln-r wh s. Th followng mhms lls yo h sory from h vry gnnng of h fndmnl fs of lrons nl yo g h nd o of h frny-rsons-fnon of h dod-m. To mk ll sr, rs of h oml fnons r rld nd rssd y symols (h mns: lf s hy r) nd ons wh h symols r rdd o s smls form. Th nd-forml looks omrvly sml, dos no sy mh n s hddn omly, h llon of nmrl vls n smly md y wrng ll formls no n l-l nd mkng dgrm of. Tody s no longr nssry Dodm - Pg of -

3 Dodm - Pg 3 of - o ll o oml fnons y hnd. Afr hs yo n hlosohz, why h frny-rsons s romly logrhm n rn rng. I hnk, h oms from h rmsn, h h hghr h n-frny, h lss hrg s lodd n r h ls.. oos of h dr on hr s rron for h omng ondrngs h drvon s shown how o om o h roos of dr on, s hy n onn mgnry nmrs nd hy r lr n h onns of h dffrnl on sng rod osllons. If w hv dr on of hs form: : o h on o lmn nw w dd n rsson o lmn w go now lly n ordr o rss nd : hrfor ws hrmrs r dffrn, h on nd s for, nd for h followng on w know h roos s know h roos, w don'

4 fr sr roo of h on : s nd n swdn hs rodr, w g :, If w hv h on w nd only odvd on rl h fors y nd nsd of y nd nd s nd, 3. Th dffrnl on of h lron osllon-r s lso shown, hogh, n nohr on on h ws: h://rh-folyn.\ Thn\DffE.hml hr shll shown h smlss rnson from m-fnon o n ndlss osllon y vron of h offns n ordr o show h rol of mgnry nmrs n h lron orns. Dodm - Pg of -

5 Dodm - Pg 5 of - vl. - h nl fold of dyd o h hs whn h volg h m, s h, nd for hr m onsns h nd shr hsm rssn nd om from, h nmrs s h for ) wh h nknown onsn h only osslfnon () for rl of w nsr y wy ) fr dffrnon of ),, d d d

6 Now s lr, h n h on nr on lwyszro for j of j os 3...!! 3! jy! jy jy f or o dlvr y hdffrnon of offn s for h dr on o hv hs roos. losr dsrd on my ws: h n - fnon of h dffrnl on looks nyhow lk : n s of! j sn... j nd w s jy y y y y y y... j!! 6!! 3! 5! nd hs r h srs for osn nd sn 3! w g h vdn for hs yo n fnd n h owr srs jy h: //rh - folyn./thn/dffe.hml 3, ) h dr on mks h ndndnly from h sl n h onn nd s w know :. jy 7 y 7! of os... vl h ror And s j sn nd os,sn do w srh rl nd mgnry rs:, now w s, h f ny onsn : f hn f hrfor w n sy n s of j Dodm - Pg 6 of -

7 n s of ol nd ondnsr, h on of volg nd rrn s h mdnz Z, h sn, how n mgnry nmr n ly rol s r of mgnd of lron omonns. Z Z j s n mgnry nmr nd rgh now w hv Z j w nd hs n ordr o sy somhng o hvln h hysl rs. Evln r h mdn Z dl n Z Z Z jx, X s rn n h s h rlll - onnon of Z S Z n Z nd Z dl S ZZ Z Z Dodm - Pg 7 of -

8 dl dl T dlon lyr rrn volg hdlon lyr, Hr yo s h hrrs of h dods. B for h smlfd mhml rmn on hnks h dods s dl swhs, whh hv n swhd-on-s h forwrd-rssn nll, n h swhdoff-s nfn nd h m nll for swhng ovr. I s nmly mossl o l h onnl rrn-volg-hrrss of h dods flow-n no h ons s non-lnr rssn. dl (srongly mrr- dndn) kt osvn forwrd - dron o mrr - volg (5mV y 9 dgrs T mrr n dgrs dl T lmnry hrg K) K Th of h rnl Dodm - Pg 8 of -

9 mhml nsz s h followng: f s h ls-frny nd h m T = /f s hos m, fr whh h rdng s rs: () = (+T), h s h sdy s, fr whh on hs long nogh fd-n h ls-frny. Th hrg, whh flows n h m T from h ls-rrn-sor no h ondnsrs nd, s h sm hrg, whh flows n h sm m o ovr h rssor gn. Boh hrgs Q n nd Q o r fnon of h dr-volg U, so h djss slf h rondond ln-s y hs. Flowng-n hrg: Flows rrn from h ls-sor hrogh h n sr onnd ondnsrs nd ovr rn m, so s flown h sm mon of hrg no oh ( Q =. ). Thrfr ms h forml Q =. U lkws vld for h ol sysm s Q =. U for vry sngl ondnsr: Q Q ol U U U U U Q U U U U Q ol U U U Q Q In h fl r hr s h ondnsor hrgd o h volg U,= nd w onn h dshrgd ondnsor n sr nd hrg hn oh o h volg U n. For ndrsndng, wh hns, w ssm, h w, nsd of, fd-n onsn rrn so long no Dodm - Pg 9 of -

10 h oh ondnsors, nl h sm of hr volgs U + U hs h vl U n. U U n n U Q U U, U Q, On ss from, h sn from h flowng-n hrg s h sm, s f oh ondnsrs wold dshrgd nd on s on h volg U n U,= hm. By h flowng-o rrn no h rssor looks rnly somhng dffrn, s hs s drmnd y U,=. Bs n vln r for sr mhm rmn s smlfon of h fl rlons, on ms frs mn, f hr fnons r n fl ordn wh h fl r. By n vln r w ssm, h hs s o h sm dl-volg dl nd h sm shor-r-rrn S s h fl r. Th dl-volg wll gnrd n h vln-r y n vln-volgsor, whh hs h nnr rssn nll nd dl / S ylds h nnr rssn of h vln-r. Erh Folyn Engr. Vnn, Asr My h Dodm - Pg of -

Canonical Quantizing of Spinor Fields: Anti-Commutation Relations

Canonical Quantizing of Spinor Fields: Anti-Commutation Relations JOURNA ON POTONICS AND SPINTRONICS VO.5 NO. MAY 6 ISSN - 857 Prn ISSN - 858 Onln h://www.rrh.org/jornl/j/j.hml Cnonl Qnzng of Snor Fl: An-Common Rlon D. Grn PhD Unvr of Brln* Ar Nw mg of hr nor ro on h