Exam 4 is Wed. April 25, at 9:05-9:55 AM. Rooms: Last names beginning A - M Akerman 225; N Z Tate 110.

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1 hm 5 Rviw Sht fr Em Pstd //8 Rmidr: Em is Wd. April 5, t 9:5-9:55 AM. Rms: Lst ms giig A - M Akrm 5; N Z Tt. It will cvr th mtril cvrd i lctr thrgh Wd. April. 8, d th rdigs d prlms : hptr 6, Scti 7, p. 9: Hlim tm Hmwrk 7 hptr 7, Scti, pp. -9: Vritil mthd Prlm St d ttm f p. f Hmwrk 7 Mthhptr E: Dtrmits Hmwrk 8 hptr 8, Mltilctr Atms Prlm St d Hmwrk 8 hptr 9, Ditmic Mlcls Hmwrk 9 S pgs - fr th qtis tht will prvidd Em. S pgs -7 fr spcific tpics tht my icldd Em. Y my rig -prgrmml, -grphig clcltr. N ts r llwd. Pls rig yr U crd t th m; th prctr my spt-chck ths wh cllctig th ms. A prctic Em d its swr ky is pstd th crs wpg.

2 Pssily Usfl Eqtis, vrsis d stts hm 5 c m/s k B.695 cm - / K h 6.66 J s! h/.55 J s.6 9 V.6 9 J crrspds t 866 cm - m 9.9 kg m p.67 7 kg m.66-7 kg H tm i cs i si ν ~ 9,678 / - / cm - E - m r ε h 8ε h m lssicl wv qti,t / /υ,t / t Nrml mds f virtig strig f lgth l:,t A cs ω t φ si / l Schrödigr qti:! / m d Ψ / d VΨ EΨ Mmtm prtr: P -i! / PIB ψ / ½ si / E h / 8m HO - / ψ whr µk ½ / ¼ /! E v v½ hν whr ν / k/µ ½ d µ m m / m m ditmic Rttil mti: K ½ Iω L / I I µr L Iω mrv Rigid rttr: E J! /I JJ E cm - B JJ B Hz h / 8 I B cm - h / 8 ci ω v/r Hydrg tm: ν ~ 9,678 / - / cm - E - m V 8ε h ε ε h.59 Å m ψ s / ½ / / - r / Φ m φ / ½ im φ Aglr mmtm: L ħ l l L z m! L z - i ħ ˆ / φ Sphricl crdits: dv r siθ dr dθ dφ

3 i i B A slti is k d d B A slti is k d d Eqtis Diffrtil d d d gr psitiv d d d d d d d d d d d d d d d d d : si cs : it! cs cs si si si si si si si si si 8 cs si si si cs si si cs si cs si si cs si l

4 Hlim Atm Writig th Schrödigr qti fr th hlim tm hp. 6 scti 7, pg 9 hp. 7, Vritil Mthd Scti Wht is th vritil pricipl? B l t writ it t, s p. ; this will t prvidd th qti sht Prf f th vritil pricipl s i prlm 7- Grl dscripti f hw pplis th vritil mthd t ptimiz th djstl prmtrs i tril wv fcti sig th ct Hmilti prtr Prfrm vritil clclti giv tril wv fcti d th ct Hmilti prtr Mth hptr E, Dtrmits Hw t clclt th vl f r dtrmit Grl rls fr dtrmits: rslts p chgig y rws r y clms sig f dtrmit chgs rslts if y rws r clms r th sm vl f dtrmit is zr Why ths prprtis r imprtt fr writig dtrmitl wv fctis hp. 8, Mltilctr Atms whl chptr, Sctis - Atmic its Writig th Hmilti prtr d Schrödigr qti fr tm with r mr lctrs r, writig jst prt f th Hmilti, sch s th pttil rgy prt Rslts fr H tm grd stt wv fcti d rgy if itrlctric rplsi is igrd Writig tmic wv fctis: idistigishility f lctrs, tisymmtric wv fctis d th Pli clsi pricipl Sltr dtrmits: hw t writ d why thy sr tisymmtric wv fctis H-S pprimti - qlittiv dscripti: s f -lctr ritls, Sltr r Gssi ritls fr R-dpdt prt f ritls, sphricl hrmics fr gl-dpdt prts f ritls. pprimt wy t vlt th pttil rgy trm fr lctr-lctr rplsi glct f lctr crrlti grl mthd sd t prfrm slf-csistt fild S clcltis ritl rgis dpd l s wll s.g., s < p; drstdig this i trms f th rdil distriti fctis s p. d "shildig" ffcts Kpms' thrm frthr plid i prlm 8- mthd t clclt th rgy f th tm t simply sm f rgis f ccpid ritls; mst crrct fr hvig dly ctd th lctr-lctr rplsis

5 Prdictig th grd stt lctr cfigrti f tm Udrstdig trds i iizti rgis crss th pridic tl s i ig. 8. p. 9 Aglr mmt: spi, ritl, ttl spi pls ritl drstdig th mig f ths prprtis d thir qtm mrs dtrmiig th mgitd lgth f ch typ f glr mmtm vctr d its prjcti th z is, fr lctr d fr th ctritis f ll f th lctrs i tm Atmic trm symls sig Rssll-Sdrs cplig: prdictig # f micrstts fr giv cfigrti writig ll f th micrstts m l, m s vls fr giv cfigrti sig this list t ddc ll f th trm symls sscitd with this cfigrti s f Hd's Rls t rdr th trms i rgy s f th shrt-ct t prdict th grd stt trm syml witht writig ll th micrstts why th micrstt mthd wrks prjctis f glr mmt th z is dd s sclrs - ig. 8. Spi-rit cplig: qlittiv mig d csqcs i rmvig th dgrcis f sm stts cmptig th ttl spi pls ritl glr mmtm qtm mr, J, d icldig this i th trm syml; rdrig trm symls with diffrt J Hd's rd rl Slcti rls fr tmic spctrscpic trsitis Rviw sht fr th hlim tm, icldd i HW 8 s swrs pstd dr HW. List f tpics ctis th t pg: Ditmics 5

6 hp. 9, Elctric Stts f Ditmic Mlcls whl chptr, Sctis -6 Writig th Hmilti prtr d Schrödigr qti fr H d fr H Br-Opphimr pprimti: hw t dscri it; wht is lft t f Ĥ; hw th itrclr sprti is trtd wh clcltig th "pttil" rgy crv Agi, th Schrödigr qti c t slvd fr H r thr mlcls with > lctr, s mst s pprimt mthds vritil pricipl, tril wv fctis Udrstdig th "pttil" rgy crv f ditmic i trms f th kitic d pttil rgy ctritis, frm th viril thrm d ctr digrms f th H ritl clss ts. Sprpsiti pricipl fr ddig wvs H d H dig dscrid y mlclr ritl thry; mig f th vrlp itgrl S d hw it vris with R th itrclr sprti Writig th wv fcti, r th prility fr fidig lctr, i giv LAO-MO, d idtifyig th itrfrc trm. Giv LAO-MO cmpsd f rmlizd AOs tmic ritls, ti th rmlizti cstt c lv i trms f S, th vrlp itgrl Mlclr "pttil" rgy crvs fr d d rplsiv stts; fr grd d citd stts; mig f th dissciti rgy strctiv r dstrctiv itrfrc i dig r tidig σ sigm MOs mlclr ritls risig frm s AOs tmic ritls. Rviw sht fr H mlcl, icldd i HW 9 s swrs pstd dr HW. strctiv r dstrctiv itrfrc i dig r tidig σ, d δ MOs risig frm p d d AOs. Aglr mmtm t th z is d M L fr th σ, d δ ritls, d prity g/ lls Grl rls fr cstrctig LAO-MOs Ergy rdrig f MOs risig frm s, s d p AOs, th i th sc f s-p miig, d wh this miig is imprtt why? Grd stt lctr cfigrtis d trm symls fr H thrgh d fr htrclr ditmics sch s O; prdict if prmgtic r dimgtic [Nt: i writig trm symls, s g/ fr hmclr ditmics, t d't wrry t /- ] Giv - cfigrti fr grd r citd stt, giv th trm syml d d rdr Bd rdr: its crrlti with R, d strgth d virtil frqcy d frc cstt fr similr ditmic mlcls d thir is; cptis t ths trds Li 6

Exam 2 is Wed. March 28, at 9:05-9:55 AM. Rooms: Last names beginning A - M Akerman 225; N Z Tate 110.

Exam 2 is Wed. March 28, at 9:05-9:55 AM. Rooms: Last names beginning A - M Akerman 225; N Z Tate 110. hm 5 Rviw Sht fr Em Pstd //8 Rmidr: Em is Wd. Mrch 8, t 9:5-9:55 AM. Rms: Lst ms giig A - M Akrm 5; N Z Tt. It will cvr th mtril cvrd i lctr thrgh ri. Nv., d th rdigs d prlms : Pstlts d pricipls f qtm