PHYS 305 Final

‘Phys 305 —— . oo Final Exam .. Fune 1995 ~\ . - __ Nei homes 3 heurs I. Shot Questions. ( please shect answers ) Qi. xf the onsrgy argon ualials H an obsecvahle form a ce qwatiauwous spectum, how <5 Lt possible be form & physically alceptable stake 2, Explah De term "phys cuably Qa. Lf lx) ds an Lrirgy Ligon funchon of an observuble and t5 a stahonary slate » In which way <t becomes Lemme — dapendoat 2 Q3. A spn-t parhcle xs plaad mwa consdand magnthe fab aleng He Z-axis. What is the pared bf Yolahen of Hu sp as dima Progaass 2, Can this folahen be cliscy ibec in quantum midanits aS pracessing ahoat As @-ans ? rf ned why 2 Oe. What vs +s uncertamty ridahen [A x), (A Ph dora harmenic Oscitladoc cn thy shale In> 2. Guive dt Vala for PSE Ground shu le ln=o0> . ‘Expdun the pry sicak moaning of the fact Phat (Ax), (Ap), do. Hint . Y ou netd a short calculahon sf (Ax)? aud 2 in (AP), by using dAs opvadar a and at. (5. Tha entegy tiyeafanchons of ths raclial Wave £4oalion wre 21, 0,b1E4m> = Ble) Vim (G4) What As ths phys reason for this separahor d/ween thy yada and angular Pard 2 Afi ineag eee “CAN UNte nner [ MRR Ap Y OE pray ee PAYS Boy Final Exam Tune (995 Tl. Problems There are 5 Problems, The Problems @, @) and G) are obligatory » You can chouse between problem @® er © Yr. Hy drogen Actonn, Given «> the wave functien 4 -/2 ps bh) ee Og Y (4 oe) = “Fr e. 1 (GP), where Ag= une he AS ths Bohr Tadurs and A As a Constant ° (a) Solve t+AL dima —aurclep endlont Sthrddinger 4 4uahon do show that W (7 &) AS an Lye function BY AL” alichun av tha hy drogas atom ) f ads spin dgrat o} druacdom AS net cons derad - (b) WAad are dha cecresponding enlcgy Lig valuts ? ) Which quantum numbers CN, bm) chavadtriee Hy she of He elechon 2 (C Phys 305 eam Tune 1995 712. A spin 4 Parhele as at dime t=0 wm the wo fA Z> Stile. L's plaud wa skong magnthe | diskd Bea (0,0, Bo) and aman Oseillahng fiald = = > B _ B, cos wt x? B, snwt qd ° (a) Show that da Hansihon Probabitity dy thy 1-ZS shle at # Ame t ds VK by 0 W_ = Us Ba su CA -t), 4 Bn 2 2 247k Where A 4 Ue Bes) +B, ws 1 Y ow assume only spn grt df brezdonn for the Pardele , that as Be Hamitlonian &s giver by : => J H=—-ts SB (b) Distuss the yasuGt oblaiwd for Ais so calle U " Paramayne hc Fesorang absorphon - H mt, Af Construching +a Hamillonian , Ae basic ASSUL ay dav. do (low Ad, kvokuhon J thy vee =( 38) This Problem a5 relahvely long } Final Exam Tune (999 Ds. The spin Hami Glonian f a spin—~t Parkclt fb as givta as cn Problem (L.A). However, the parhile | ds placed in an wernal magrahec field : B= (0, By, Bo), whore By >> Bg - (4) First, didecming He onirgy bigenvaluts biaclly , | (>) Then , cateulale inthe frambmork cal Pydurbadion tree ds Sntrgy bxgenrvalits though second ordt- An B2 [Bo , and. compare ths vasulls ant He Axect values tn prt (a). Do you pnd agreemtyt ? Llints - rn part (a), ducing Your dip adfink tly = = fs By and 4, = - Ms By Tn Part (b) > Your trip as not Doing Ay tad before second —ocdy begy shift. Tu. A molecule rotates rigid ty wa Sspag about af the origin ef the Covcdinale Syskim anth two dtara of frtdom disertbed by the Polar args re) and cf ° The Ham tontan a's pve by LI = pr ) Tez mMemént of nicha AT : (a) Find He Ut veluts and Lagoa func tien and thir possible digentracy _ (b) At 4 given Aime , the rodator As tn the shake W(Gp) = al coe + SiMe Cos2d) white oo és & normali2ahon conshint (stad 2 r4 12 As mgasuced what ts HAs peobabibihy of dindwagy Hye values : ode and © (ao) % (c) rf A SemuLtangous measurmint of 1° und tg is dent, What ts He probab, Gly. od. finding thy vabuts (€h",- 2h)? Llint. Fake a Fook at Hs sphniwd harmenice on Page QC€ cn te book . Dane 1495 Ts. Co ld Emissiav Ham medals ao TH is bprimintally known that an applud shang tlichic hud necmuf Ad Hy surfacé of a medal Atals 4% Dmission Carrlrd oud sels the metal. The Liphanahon 64 this Cold emission effect " As Possible biy the dannel effect . Aceesdiny +r Ha Paubj Principle , the as conduchon ehucdons occupy at 24¢e dem prraha rie (T= o) Dy fonduchon band Up At PL Ferm — Engg. Ef ( see fegure). The work fancdon A's defined as Wea=Vo- Ep . The effect of thy acdynat Field is As change the Polnh al Ve dd VOL) =Ve-CEX us shown ch tl de gu reo 4 ts reasonable to assume that the elecdune nar the Perm —sacface leave the mutel , sinte the Lunnel clishnu ts As shorkst . Ca Peutale thy emission Curréut > | €=€) as a danchov al Wo and E, and Jo ‘ a Hint - see Equahion (6. (59) as a shavhng Point