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# LASER PHYSICS PHY 395M

UT

GPA 3.77

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This 78 page Class Notes was uploaded by Malvina Orn on Monday September 7, 2015. The Class Notes belongs to PHY 395M at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 60 views. For similar materials see /class/181827/phy-395m-university-of-texas-at-austin in Physics 2 at University of Texas at Austin.

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Date Created: 09/07/15

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VHF WuL W weI 1 CW WM CZ 947 4 magi Mr W c 1 91 L 2 y 4 397 w 3 2 whiz k 9 H 301 I gtgt 3 i a Ian M s v gram 141 IR QM 4 VJ Wad ragawit m 314 5 Be 611 43 5 my ya x W x l ci7J t wm I HJEMH e JH6WRICamp M x I m w A 39f w m 1 who lt w m 00 mg owl0 HZampu VEGA wzwl T E 46 8 Mt Ms Mu 39 O 139 quot 7 M 9quot rrzr awewary W1Ww 1 W0 WU 2 beam wau srquot WWI quotf ze quot M7er Winr39mw 1 2a YE Hed ny cu I 6 Wm W 23 39fs 777 3 Lian ask an gel m nrnml Ggt 1 97 3 foalm loss P 10 W7 W K Ruby Rod 1 com End WW ye v edv w canhhyo HF 0 m A2103 amp P4le diam Lx T farAWE Chroma 7 C WM T 9 Cr 1w kw crMJ ash I noquot Aw R w me lfabk M T x 4 m 5 M 6773 r r V39 IRquot Exmf z verad zum WT If medude m do qm frcmsiemf 39nWszm M fai cJ HEL39M gtNevv W m LvL W 9 W ium mi Mm baa m AI 70mm aid f T d HR 395 mania DC BM m E 2 50 MA Ag window 7 L F M LannMiu m HE Neg IS IM39U Im A 32 m 1 M2 0L 7M 3 gt 327M 7 Zpsas an MS uff 1 ZPEW 215 a 7 2PMquot Em 2 53 DELL P Iquot d 99 70 new a J 3Ff35 Eguilibrw immme 0 Selec vg CXC 45 Z 6 lg Mam quot 7 Mm Neon oh VI151mg QMG VG44 He hun W T E quotlent day we 4 90 I wn us m Mmquot QM c quotLu Lg M0 1553 quot 5041 MAPAG Y I m 37 Emmaquot AWL PM tom a ms W quot5 I 39 mquot h e 6er 35 5 wwwhmgw J emuAm 6471 W 1w mam kilni m m 7 71 WW deep W X Mdg mmwm e uh 7 17le jam 2ch In mfvlwwmbe 411v m m ES 5 m qm 39 in 9 Mm Wi w c w1 r 19 most abowz MAM CM J52 QXMM URL rezuem JoulaiuaJ y39fln v Mfiw no 39linm orggisimcw mg I 302m 2134 also V Aim Mic L Malem m SfauHOScafy may L192 1ij lad 21ml lye Arr 775qfrAIrQ cl 7 0 eh wfrli Mg6 39 Bes umble IR lauL Souf e a A gt 4 5 MIL H L Algae o u wf I 1 115 MNZK w 51ij 1 VS e L07 22504 Hyper ne Structure Nuclear Moments Due to their internal structure nuclei have electromagnetic moments If time reversal T or parity P is a good symmetry it follows that All odd electric moments are zero and All even magnetic moments are zero Parity is not perfect symmetry in nuclear physics since rather substantial parity violating effects are seen in nuclear beta decay for instance However time reversal is an almost exact symmetry and as a result no exceptions to the above rules have ever been observed It follows that the lower order nonzero moments of nuclei are magnetic dipole electric quadrupole magnetic octupole These moments give rise to observable effects in atomic spectra called hyperfine structure These effects are small but are very important in many atomic physics experiments Also careful studies of atomic hyperfine structure can be used to determine nuclear moments which is of some importance in nuclear physics Nuclear spin A nucleus has a nuclear spin 1 Since a nucleus is a composite particle its spin may take on an integer or half integer value The spin state of a nucleus is given by 1 M1 where M1 I I The square of the angular momentum of the nucleus is thIl and the 2 component of the angular momentum of the nucleus is hMI In advanced quantum mechanics courses it is typically an exercise to use the Wigner Eckart theorem to prove that a 2 pole moment is zero if I lt ld2 From this result it follows that a magnetic dipole moment kl exists only if I 2 12 an electric quadrupole moment k2 exists only if I Z l a magnetic octupole moment k3 exists only if I 2 32 etc The preceding conclusions apply to any nondegenerate quantum state of any particle For instance a nondegenerate state of an atom cannot have an electric dipole moment since that violates T symmetry Or a 281 state of an atom cannot have an electric quadrupole moment since J 12 lt l Electron magnetic moment The electron magnetic moment is us geuBS where ge is the electron gfactor geEZU 0c21t2l00116 1 Since the spin of the electron Sl 2 the electron has no other electromagnetic moment It was known from early studies of the anomalous Zeeman effect that ge was approximately equal to 2 One of the successes of the Dirac theory of the electron is that the value ge 2 naturally emerges approximately matching the experimental value The fact the g6 E 2 is somewhat surprising since if you try to model the electron classically as a spinning ball of mass and charge density and make the assumption the mass and charge current are everywhere proportional to each other it follows that g 1 Actually it later became apparent from both precise Zeeman effect experiments and from atomic hyperfine structure measurements that ge deviated slightly from 2 The situation closely mirrored that of the fine structure while Dirac theory gets close to the correct answer there are small additional corrections in QED which do not appear in the Dirac theory For the case of the electron gfactor the leading order QED correction is x 11 As we will discuss later in the course the electron gfactor is one of the most precisely measured quantities in physics and its value agrees with QED calculations to very high precision Also note that there is a sign convention here such that ye geuBS and ge E 2 We could have equally well used the convention us geuBS in which case we would have ge E 2 Unfortunately you will see both conventions used We will try to stay with the first one in this class The negative sign is meaningful it implies that the magnetic moment of the electron points in the opposite direction to its spin Nuclear magnetic dipole moments The nuclear dipole moment I g1 u l where g1 is the nuclear gfactor and u eh2mpc memaul nuclear magneton 5051 X 10 24 ergG 2 with H Bohr magneton Since the proton is about 1800 times heavier than the electron this implies the nuclear moments are about 1000 times smaller than electronic magnetic moments Note we are using the opposite sign convention as for the electron so positive gfactor implies a magnetic moment parallel to the spin The lightest nuclei have spins and gfactors as follows nucleus spin I g1 proton 12 55 883 neutron 12 3 8263 deuteron 1 085742 3He 12 4255 4 He 0 The spins and gfactors of all stable nuclei can be found in a table of the isotopes As is the case for the electron the fact that the gfactors deviate from one implies that one cannot understand nuclear magnetic moments in terms of any simple classical current model Electronnuclear magnetic dipole moment coupling This is the dominant term in atomic hyper ne structure It contribution to the atomic Hamiltonian can be written as 1 A A 87239 H L r 3 mm n 7y 146 3 The interaction has three terms which we interpret as follows First term The electron has orbital angular momentum hL As a result of the electron current associated with this orbit the electron generates a magnetic eld B0 uBLr3 at the position of the nucleus The nucleus interacts with this magnetic eld according to H all130 HBr3L HI 4 Second term This is just the interaction between the magnetic moment of the electron and the magnetic moment of the nucleus which should be familiar from classical electromagnetism Third term This is known as the Fermi contact term It is an effect of the nite size of the nucleus which we can understand as follows Suppose that the nucleus is a spherical object of radius p0 and with a magnetic moment 111 Since it is a dipole the nucleus will give rise to a dipole eld B N ulr3 and this will give rise to an interaction with the electron magnetic moment that just results in the second term discussed above However this dipole eld will only exist for values of R gt p0 Inside the nucleus the magnetic eld lines will have a different form To keep things simple let s suppose that the eld lines for R lt p0 are constant in magnitude and direction as shown in the gure below magnetic eld lines of a nucleus I From the condition that the magnetic field lines must be continuous at r p0 it follows that the eld inside the nucleus must be Bin ZHIP03 5 Now we can divide the expectation value of the interaction Hdd between this dipole eld and the magnetic moment of the electron into a part arising from the interaction when the electron is at a position with r lt p0 and another part when r gt p0 Had ltHddrltP0gt t ltHddrgtP0gt 6 The term for r lt p0 is 2 2 pa Hm lt p w B lt gt 15 Mfr l W V p0 po 7 7 ZyI 47239p03 87239 p0 3 llI0 l2 T E 111 llI0 l2 E u where wr is the wavefunction of the electron Here we have used the fact that the nuclear size is very small compared to the size of the electron wavefunction If the electron is in an sstate this implies that wr is approximately constant at value w0 everywhere inside the nucleus If the electron is not in an sstate then w0 will almost exactly equal to zero inside the nucleus so it can again be taken as a constant Since the expectation value of Hddrltp0 is given by eq 5 regardless of the electron s wavefunction we can replace Hddrltp0 by the operator 87239 Hm Hddrltp0 lz 1115301 8 which is just the Fermi contact term The term Hddr gt p0 is just the second term in eq 3 apart from the restriction on r However if we just keep this term as in eq 3 and allow the integration over the electron coordinate over all r this term will have the same expectation value as if we kept the restriction r gt p0 For s electrons this is because this term has zero expectation value due to the average over all relative angular orientations For electrons which are not in an sstate the part of the integral for r lt p0 does not contribute to the expectation value because the wavefunction goes to zero for small r so it doesn t matter whether we exclude this radial range or not Therefore we can leave the second term in eq 3 without any restriction on r Order of magnitude of HM 2 2 HM Jig fawwiij m2 9 r 610mp a0 mp The hyper ne splittings in an atom are of the order of mep N 10 3 times as large as the ne structure Hyper ne structure of the hydrogen nl state Here the nucleus is a proton which has spin I 12 Thus a basis of states including the proton spin is lnl 0 ml0 mS ilZ m1 il2 There are four basis states corresponding to the two values each for the electron spin and nuclear spin projection quantum numbers The expectation values of the three terms may be evaluated as follows lLu1n lLln msm1l1lmsm1 0 since nJlLan 0 in an sstate 2 301 lJI l u uI 0 for an sstate Due to symmetry this term averages to zero over all the electronnucleon relative orientations 3 Fermi contact term This is the only nonzero term for sstates We can rewrite this term as 87239 87239 HW z1115301Tgm3g1m1853R 10 Oras Hm A IS 11 where for the 1s state the hyper ne constant is A lWIs0l28n3g1geHBzmemp 12 We can also write this as 3 Rya2 g2 4 L 51420MHz 13 h 3 2 bug Km2mp where up gpy 2 is the magnetic moment of the proton Aside The momen of a particle is de ned to be the expectation value of its projection on the zaxis when its spin projection number is a maximum Thus the magnetic moment of the proton is u 1 12 M1 121 p121 112 M11212 121 gpu lzl 12 12 gpu 2 14 Now the Fermi contact term is proportional to IS We could find the eigenstates of th working in the lms m1 basis if we wanted to but then we would have to go to the trouble of diagonalizing the Hamiltonian matrix Instead we use the usual trick of anticipating the correct basis ahead of time We note that the total angular momentum is FISwhereFlI SlISl 14 For the case ofthe hydrogen 1s state we have I 12 and S 12 so that F 0 or 1 Also we can write ltIsgt 12 FF lllz ISlZgt 15 If we change from using the lms m1 basis to the lF mF basis where mF F F is the projection of F along the quantization axis then the Fermi contact term is diagonal and we have that IS 12 FF1 111 3s1 34 ifF0 16 IS 14 if F1 This leads to the following structure for the hydrogen 1s state H day 2 EL M R napav fansm w 4 g I elem7m Imam gt ll 1 Ma 1 J sgain I FL 2 I 55 ea E Hawmm H 1 I 1 v 1 UM 1 71 7 I Vx 2 duhquot laugh a qB t 2m 7quot Z c g 1 u 1 we 2 Va Z gxhvh c ed39rm a le Mume quotii 7 vi i 52 clamMel mm mm l V fr 2 1 VW 7 E 4 ve MCWV MMIN C ulmL mk u n V New Va1 7m rise h biuirwi crl dim WM 17 ML gladwe L ny llmcltr Lean7 rnw aedwr Amp Swill M Mama 50 AW 1 ASSw L mum 15nd payihm f m 9 A N H39H rmi7 Q 10 Veg r MAO 12 Hamlhnnw m 991 M DchL m 1 a 7WWEA 2 er Fw cl elemng bula ew mkfle eHL rmsme Egdki I Q d e a N M a rm a Egggt rug 6 m 1 2W1 Mum mm A JWR armJM q wwg mt N IAghew mggnqh We 55 know g 2 N 37 mi 5PM 5 an wt 23 E L m I K armm Cmquot w mi fo mm m 23 e 1 If 3 5 kq gwsmmw mFmoj nin L 33 Enisi 3 mg h EILMQ nyagz s 5 3 I E 1 9 I s 3 ma 5 u we me A IEHAkKnlL NSF xx KnanSffm xxnr r Z31 mm H ELmax Exnltmmxxpauv meoLk ox LITE Fun m i WMme 3 TEE W W58 ax Jv 1hr I in ux F Irma MJmi 1 mx ELmny x Som Ruf alk ms xn mxlmpn 1 U 4 3 t L V l ltm Pp H K f WWNPV xi sir amatus 953 53 ptsnrv Eled vmic enw e39Fng iwj a a q a n yingHm h 1 hhwf r ql 4L Mala quot Vquot Z VHme Drawn lolev f N m amp rm V6 21 Desz w Aim fin7 6 may ma mva L5 Ln as w nnxumm SIMnunquot Lnngxuul 439 RM 9mm a Maw Sim Exawfll39 H1 Alumnim Patemull 15 L Mlemle Palm m E 5M9 r 3N hudcw Cnar rwib u tznm c MAHQL Wiw h m 5 MAJL agw ngjm 3 Hg kw MEL aft4 Wdte vgq 7 3u 6 M 2m MMJ MM an Num CuIDrJIKatJ 39 Frwl mmW 0 V E quotquot xwuul Y 13 Power garlc V V 1 P 13355 w M yr Hm kath Z i 7 E c k 1 k it 7th 2 141 Morm Maiaquot 143x 5 Am 39 w Pl m au 7 mer coonlma e m r 39 M I v I mmr hrmhm i c d e 5 emgt 5Mme 39c 561sz 399 0 H W an Hsmmin39c gmrrl T T 0 O 723 km WmJ 3 T 7 LBJ kmz 39kvvd39al WW Er move cowrhcahd quotSW1mg H s r ll PPM Indy 172 4 V12 21 wifa eff u ierTl Z lXCCJII Ww xam ola 39anurmqvu Slum r nucfeqf mnh m AnyJ Wm 46 All 6w I39mchow nu vm H122 a E EaEv M M W 5 ML Ha z mum ms Em N M M R EVE R B 24m E gure 31 Internal coordinates of uomformv Figure 33 Ab nitw ccpVTZCEPArl chromophure surface in erilinear Inca q CH stretch and normal mode qh CH bend coordinates Contours m at 2000 cmquot Intervals The anisotropy in qh becomes signi cant abova 0000 cml FmM Kola wahs SNJQMWI Thurs CM Cm mam M1041 32 a Vim WE Esqz z Cemh39nl we Frau gt7 b um 7449 w E mm WM 7 l4 HAM Wave Fwd CM 7w ckwa qulf emn Var 74 a 3930 web V02 2 MNV alww gt Ammg r H h 700 banrJa 55mm v x T D eva 0 RNA am A rammm t The L1 W 5 Ham 2 gquLV39M At t K5 R 1 4 h Load 47 grit van uv by W Q Y Em 1 TM Zr yrn 53 anca Em quot HM WM I 2 2 MWJL bi mt g 4 x 32 Zr 39 EV 91 F Bun L r 39 1232 aw SPncf39rw Karl Rom v ga E ENV B 301 ng Lasf FL R LI ulRY 91 Qo A A1 1 ER Juno EM R A my AF quotmam gt i 2 1 AMER Re combine Ra v 55mm mol 1 Be 1 E D Em EN 70 any gt Z gt EU 11 ltVIEZIVgt V17 EMT 03 EMTITHD IMHle 9 3a if 5312 Z Vafah m W 7 L7 7754 21 AQu nuwtmrk Wage J g Iva milk wave 9 helm 544 Luh rguy I E 3 V L I Mum we k0 im fi A s brh m WM MSGL Ann L H CO m a Am mad std mind Moleua ol Sfadrq 53 wk I quot11 Wis 2 D ransi m ma gaudy Km M r 465 L 45253 H 1 231 Drsxacmtethw R Safarka a mm law 9 Yo vibrakiol an nn Aisswhtfmq Eaes 6 p Pure roh39ms m TQNH guru 395 XVZ Qlec f39vnm c 5mm 5W gm ecu g 6 Aiiquot om dedmm39c cxm39chi 5w WQL a fut MUZQK iamp1 filt I 25A 5 had SPin aluma A fry ech gm NJ awful momat idecf39 m alum a z39 41 WMAQW 01d Inwwclem axis mumm vam w A 5 0 I L 3 39 zma QMm 22 S P DF A m nm c Arks AM 592 A o MWE 2 Sui s 1 A 1 1 377 5M 39 4 6 51 Wm Wang 3 wwx ear gtlt 2 new WM 2 em AW AC2 SW 12W 17 MAM lt QLdr fedLeff 0 re ec w sImMav 0g duan wave mc m 3m rek rs f Avmsiw jw dv j eec m wow GAuCHN 18 Nr D iv N39 i m SSTAZF M s N39i m x 4 i g Molm u 24 quot i 1 P m s N r mire C Ahd 33 39 an di sgacia on gt Q limb h x 34 Aw 34 quot 3 N m 2 and 1n NiD MD M l 10 W N s M s E a ma moi 4 lt01 eV lt L V i 39lt LI 3 n V i gt i i i 04 03 12 s 23 3 3x 20 24 iiuinuwleui uimnm A Figure 313 Pulcnlial energy diagram for N compiled by F R Gilmore refuelAc s Reproduced m permission of F R Gilmare The Rand Corporation 1 Exampk A an optical Moluulav SFccfuwi dais linns is W W Cvmrm ec 0 afarn1 x ch m omario 965 c Spcclrunl ofiadinc mono uoridc This is alypicgl oto39 uansilion coniaining only a sim 1 p branch and I branch structure 3 A Duri39e Can J Phys 44 139 1955 Reproduced wiui hc permission 01 th axinnal Research Council Canada a Spcclrum ol39 rhodium carbide This is a 1w sransision so me Q branch is absolutel missing Each P brunch and I hru IV w I vn quotMum quot 39 39 39 1 mm and I Hm 39 39 39 hung at some oflhc lines sec scc on 7r A Lagcrqvisk and R Scullman Ark Fys 32 481 1966 Reproduced wim permission m 0 er M Trudiw Afpolc Moifix chad Jf f F dE39W T39M evrm Actat 1 lteV7J 7 l 3 HIT1 g F F awn MIME A V C i L 12 ML m g e v TMgt 3 q 393 E AmerJth aw 1 nyk 9 I I o 7 64 am WWW 1 zfd 1EgtltEI giz JyfanReM Cam eth AhW quotIquot quotm 12 J 7 1g VTIO i kf n namep may em a aa n 129 HUS 5 may M 1 TE 1 quotW W a I 4 3m 2 m MalaJr A an a H Alelt5 magmas n Rpmr gnawu y2 K 74 a fki a dn l fgn 0219247 Wg y Ygzsiw E9 gt1 192 Ymmm fpfzrRIfol Ia e yl Iza 7f2 9 39 f E sF1 7 LL fdkffzhz wryQ LLKW 56735 A wk szw Cm Aw run HA ew39u39ul Rio 7 Q e 1 equot 69 A 6V 1779an if iR Ldum L The EQIFLI aL xeu Hgmanuplarw AiB 0 Hammad 643 310 Ly Immjlt7 77 j M IWRARED TRAAxzrzous FcR Hmouuuaqe ngu Lg E0 damL M 7 M2 j El quot0Lka Wenmi g maC L 7 7fme MD7 H39N1IGE Lean kale Lf 2 5 0 w R Z AM 0 Ilka u gt 7 ahgtlt AIPEIE d V 3 reim u Abra new In woleculi p344 149 Fw 69 0E gmjz HwyIi L QIW 40a g39mecog swag luylkj w 71 a if H K is 099 Vt A I 39Sinecusf 4 z A om n W may Maw FM For a 1M JUL w M 1 9 Iiu do S39elcnh w alas o i E II 2 Q975th quarpikm La J T EHR egua rmnl mu Ffm 2399 r ML of Maw WW M 3 SUMRT 501437 1 N17 1 35 c 2315 9 T 15 a 243 My I la 04 73 m or 5 1 SAW HUK gagin DWI 16 hquot FER mfcmwmL 5 and 6H e3 HCQ 73 2 zagg 7 00 g a 1 51539 CHL 34 quot quot y quot Slaw ICJ IkqJm mam y mhw mam frunIHu kr Lj V V 0E HR MVT1RJDRMV2 m LEWigi gg AW 7 My q II R AW 7 Diglt7 r M RIM amp 102quot Jim dgm zIJ R z voidv ltv MM l V95 i 43 uv R 56 a MV 0 ll L ltv I v dome ADltW KR elvgt Jltv lk 2lvgt 391 V M 2 W ng 0 5w v39tl v viz Trmhih uw am m g 5vt IVZEZI ix24 Y ef c a qu Inf wad quotouww quot ova U lec uw rweu LayLu Bumrm w 1 5 14quot real x ikow HCQ 9pm 0qu grec ra wI H jm x7 yum INK N0Hkl 1 Ihw miw J 1373me q vahMI NLbVAI PMML 33 H ATEth Q3hgtbm L VP HRVMAA Lm luh L933 h m 3 I ab 1 a m AICbm Ix hh r NAB I Lbitm h 2 ka L r w my u w I I rt 1 l mum owe 77 SPECTRA IN THE INFRARED REGION 57 04 039 g gm to 118 The last column of the table lt5 E gives the deviations from the formula e m g y 288590 20577m 030347 2 1 00022271 II 11 a R which now represents all the lines very Well except M nci 39 amt 39 The isotope enact Elm p 142 in clearly shown J vnllme c the lower state Hon 7 111 m 12 the third infrared band of HCl 1 3 in H 9 whose spectrogram is given in Fi 33 the isotope splitting is much larger see Chapter III Fm 34 pm of the Absaxpcinn Spectrum 0 HCl in the Eu Inimed mer Curin 173 The nrdinnm give the trans n n Ihl gm Thus the minimn mnespond to the 115on mm lmrs The numbers in pamnthueu are the m value The male ln degree beluw when to the spectrometer rend ing The wm39anngth scale is given above section 2g rtnd it appears therefore to consist of two overlapping bands one due to HCl 5 and the For this band the separations of successive lines very much mor 2 idy than almost formed Again a formula of the form

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