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hws06-1 - PHYS H5 8 Homework 4 PROBLEM#1 61(4)6 have an...

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Unformatted text preview: PHYS H5 8 Homework 4% PROBLEM #1 61) (4)6 have an eleoirm in a HyJPOfM aaLom (“JUL wwermm 1m; e, 91) = A (‘ tad—V252,] my $1.45. 08 wand +0 Chad ‘H’le HarmaliEml-ian Qatar A. 1-? we can express H115 Madam in spherical harmnics bar We will be easier. Ham 62F} Ff EH15 Page [39 we hm WW9 95) = I 3 V1 5 e 131% ii ’ (2m) m so end-141 = 1% Sme{e‘*—e““5) 37T. _ 414“ +>4 1) z 2; ‘51)” 5.069.491 _fi; (___ grr)/?_()/ y+1+y14 ) = 5-1146 510?!) [/5er H115 we can ('8.- «press "”18 W‘thhon' #413995): )V2(x”+y‘) re -F/2 5(3 ”1’ New, +0 101ml A 0/6. Cay/J Qua’ua'l'd <1H¢>by doing an inLegFaL bod“ fhereé amwh more efficierflL may. g? PHYS H58 HMMA *7; Problem. ’71 423+. The +I‘ick is 40 £2:me ’4’ in Jrarme. a? hydraam enegy BWAmLES |fl£m> From GPEFFIHLQ We ’54 we {'hm‘ H18. radial panther: for n= 2 i=1 is QAU‘) = __i_ 42:3“? ear/261' fl - $- 0 I“ r e _ =. V24 (L /2. Q2: CF), Theréforg) IV” = A _1_ gay/2 Mai/1M1 >41) Q1. 2 3’ 2 A: EBZ’JJA. afis/z (”+1 + 11) R2: ._= A V/é/T (2.5/1 (WM->24) R2. “4/ = MW .5):— a.” [1211>+121-1>] .586. we know ‘Hm‘f’ Qwherz. yap W 574’! gun/[y 'weiazm'ecl sum of +0 orjrhtgoml Shite-'35 H16 Mal is normliZcJ When H16. ' PFe-Qxdor 15 iii/Vi) 55 we I’M/vi A516 05/1 = i =1)? A: 6—5/2. 1 _ “”4. ”E 42 03:27: (Juarez 11:6 dropped Hag Enter a? i because H— Ban/es an unimporkmf phase. @{ PHYS H5 B .Hka 1% Emblem ‘* 1 (La-rd“ b) CaICu-IQ‘LE <L2> (II/mil <Lz> From PM 61ch law l¢>=_VI§,(I211>+I21-1>). Since '4’} is; at SuperposH-‘Ion 01C 544495 which all have 1’— 1 we know (Ll) = HIM +1.) = 2132. Since NJ> ism eggs” scopérpoaihon o-F 4-3045 Lui‘H'l L2 = +1. and: L2 = — 1 we know <Lz> = O. C) FmA H18 Possible med/Saree! vaiugs £3!“ L2 cam! Lz. L2 The value is 2?: (4);“! proMJEIhLy= 1. L2: RasSiLJe values are 1"]; each wiHa Probabih'l'y 991:1] +0 V2 PHYS H5 8 .I-Iomework 1% . - - - Daniel SM PROBLEM *2 - 24-May 2008’ . Us 0,011.5:ch .+¢uo (AIS'I'mgulSI'M-IJIQ) PMI‘ECIES OI? 1111465 m %1 bond ‘I'o ans dnovLILe/{f by a farce FOP): -I4r The M‘I‘ICIGS .m Cons‘I'ramecI I?) move 11"! 61 PIG-n8... O.) UFII'fi CI-OLLIYL.'H18 IlemiIfI'dinian gr Has SysI-em 'm Iarms of H18 sepfiraI-‘wn beI-ween 'I—Ixe FurI'ILIeS) 7", and Hue momenI‘um can; mafiI'e 'I'o' I: When we 51;“de Hue kercgen a‘I'om. we IsmaeJ HmI' any ‘I'wo InocIy ProbIém 3.anij a CanI'f‘aI farce can I38- "I'M/:15 farmecI inI—o a i IJme pFabIem w:II16M (SK-I'ernal Po'I'en-I'laI. TIM. HmiI-Iomm 25 H: (PE/2,“) I'VU‘). In 6m" €458 VCC) 2 V2 k r . I?) new we: wm+ ‘I'o wriIe H in Ierms 070' 7LIL€ POICDI‘ GOOFCIMCLI'es OFOOFZITaginMy15ingIe Par-I-iCIC. 1:9 cIo H115 hoIe 'I‘I/IaI' P21"- 7L}; V9: In PoI a4“ CoordinaIes. V is given by (back Cover. of ériths E'IM book) : PH Y5 H5 8 I.Homemnk #52 problem #2 Corl+ C) Now 5110;.) “10+ L2 = "Lh %# commuchs (”hum H That’s rectify mug? +0 Show H inwlves 4S only in 'H'Ié’ {-erm __L if . Since L; :5 &“5+ ConSJth': Hm: g/94 r1 97:1 'Hue. only H1165 40 Check is 0211-2151:“ or 115+ 9/99! Cdmmulttzs miH/t F11 $1.. or 1% George , I‘ll dads, became Psmlia/ Jem‘vahves 025“! resp:c+ +09! mi” Commwle wIHI I/r‘z. and Hiviany wiWQ. . 9727' A) solve I25? H16 gf‘donc‘ 5+0L‘l'é’ was funniml’l 711:5 '15 8d$l85+ +0 do PP we {Oak 6d” oar 4‘3ch five. one lowly Hami ”onion IN. CARTESIAN COORDINATFS H = Ea: + ikr = 5174(P”+P’2)+2LHXWZJ 2F. 2 = 2 I '2 1 {EL/4?: +_LIQX)+(; P), +2ka) T1415 l5 (fluent 0.. Sam 015 +wa'mciepmden1L i Jimmsiamf SEmpL‘ harmonic (gradual-ow. We know From our experience wiHrn H19. 3‘13 dea 'm . .0. bax 'HnaTL ILL/1116”. a Harm'HaniaM breaks (4p inJro (2 Sam like 4415, Hue energy eigenshie W-Funél-[ans are gasf pmdamts of 'H'us .imliviclaa/ i-DimmsioM/ megmhona L22] PHYS {L5 8 Harfiewérk #6 9le #2 044+. We, know ‘Hwfll 4416 8:..l‘0unJ SLd‘lé’ wan/e Funchan 1cm!“ a. _ 1—D harrnoniic osci/lmLor is {@r;£.cii+hs' 2.57) 3mm ‘H’lié ram-Lion Aces mi} Jamel on I}; we: hm Lz 441(x,y)= mag; 3Q = o .50 1P, 1.5 km Eigens'lfl-e of L2 wiH'l eigenvalue O... + [3] . . Danie! Sank HY H5 Homemrk #- P S B# Q 24 May 20% 94203er 3 ' a) we have 62 Spin 2 am] a Spa 1 PMHCIE I which Comblne +0 have. +0+al 60:13:“de Momen+am ? 213.1 CUI'H’l Z—Componm+ TI. Us (dd/UL +0 wri+€ ‘qu 5+a+e ‘m +6rm5 Ont-“Hie SHE/E {Md-Sch? spins. firs+ 0-? a”) 1-? +119 +2421! angular Mamm+m L5 2%: H181}. we know +1401 H16 +a+al angular Momen+um git/(Mam number is. J: 1} % because , “‘I‘ohl angular: mamaul“;I [or "59mg E 1'11 c314 + 1 ) There is an. annfesrhnrxj’e Sloppiness of {mguafe wLIwor-k have... When peaple Say "‘I'o'l'd'aflg afar Momen +£1.01 fl ‘lezy're e3+ker r‘ePermrfi 42; He Cigmvalué J. or Hue gammy "Valid-H). ij have +0 REM? 00+ (Jami People mean Jr 'IrésiS'l'. . Hut!" +th be: Clear. 1.09;”. be 01844" by Calling: J. H15. u‘l‘dl'al angular Momeml'cim gamfitm number-f! anyway, (Us I know GE: 1 and! 0+2: 1. Radclirfi a +4516 or C(cbsch? Gordon doemciefis agr- a spin 2 and spin. 1 [Garfield gives PHYS “58: Homework *% Problm #3 Con‘f' qu yoa clonfil' finders-Pam] how +0 use a 471“»: as? Clabsoh Gordon; C08 Whig-H‘s +0! readmj Grippiflj Pagfis [84 ‘ ”38. i Th‘ls 4-0ka acidi‘l’ian of angular momen'l'a} is Pmbably “HM {1445' osmium? Effie in Hue (lemme mosfly because Hm Mitzi-ion is So Comm/o £24. I? yaw need help Come 4-0 section or office hours . [email protected] ucstc’Ju +0 arrange a: med-hf. e The Possible Values o‘p 555 . £61“ “'16? sp‘n’l 1 Parhole are 41 , O, and 1 wiHm Probabilihes 3/5; 3/!0, and 710 respechvdy. b) flaw we, Pid- er 5pm 2 Parf‘icle. 'm (3.5412’6 wiHa SE =." “213:. and H16 5PM. 1 Par‘l'lcfe. 'm 52 5‘13]? thLI 5; = Jfi. In ‘lLdr‘ms a“? J; am} JZi we Ina/m9, PHYS m; B Homework #6 ' Daniel M a) We have: +000 EdemLica.‘ spin l/2 Pach/cs which have {vial angular mamenf‘um gun/mam numée/r‘ 1 am! Z Camponm+ O. In o'er wards, 0[=1, oiz=o. we wad +0 wrhtei Has .‘m hams a?“ Shy/e Wide Spins. [5% gal-aw JI=O> = [5% Is‘”=:‘-‘ 5;”=-2'->/vf + IS“’=é 52’ =~%>IS“’=2L ':’= é>/VE OF, M More 00ch noJ‘di-m) l6‘°=é “’——‘-"—i,32_=o> .—.- |+>IL> +1L>M> \Fz— new). (page “('0ch 1+ch H15 PMHcles have Hue Same 5Pa+ial wows anchor/L, Thereflaml Our 5421118 '15 Now wai+ aLuSIl 0. Same}. T118563 Whales .me idenhccd So Hue 5117546 qu> W Jae/Her be symme‘h‘ic' or anhsymmeilpic. PH Y5 “58 Homework ”5%. problfim “4 04+. Since 'HLe pabwLicles are slain V2 Huey mud be fér‘mioné, 60 Mb) 5115014 be anfisymmé'I-rfc. Haws/v90 H16 I I SEA-e 1’45 we Awe I5 symmefl'f‘ic ) so H' is no’l' 0?]!ng ‘93P hue «Damion; meagre.) H13 .SJ-aJ—dmmf'SW'lmL : 'Hae whale; are in 1% same smeIcJ s 4rmle am) I’M/V5 i=5“ 0;; = .0 We ConJ’l'achcfl’or)’ ancJ I-H'te. gh/C'WL flake; is 'impossib/en b) flaw we. pd‘ Our 'l'wo pad-Ides in Hue 5199.193 I‘D”) Since 'Hae spam! PaNL is symmefirk ( [901% pamLicIes [mu Hie same Spaflal mpuflcflon) we ”105+ aan‘symmgmlrizc “‘8 6pm 99H“. H>H> .—::- H‘>H>-H>H~>. - w: FEM Gdlxilrhs 41%? Hais stLe is Info (ii-=0) E$Uivalany I yd: Coo“ Iufid 'Hlé.’ 0/5;be “61».(1011 'ILZLHE: [DID-1H: é>1é~é> =V12—J'10> +Vgloo> |L>M>= [HM é> -———F {10> NE ioo> go I+>n>+tL§|k> z loo>, E E ...
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