講義教案詳解tut 11 quantum physics

EE1002-PHYSICSFOUNDATIONFORELECTRICALANDELECTRONICENGINEERINGQuantumTutorial11(WeekAphotonhavingwavelengthλscattersoffa electronatA(Figure1)producingasecondphotonhavingwavelengthλ’.ThisphotonthenscattersoffanotherelectronatB,producingathirdphotonhavingwavelengthλ’’andmovinginadirectiondirectlyoppositetheoriginalphotonasshowninFigure1.DetermhenumericalvalueofΔλ=λ’’–λ.Figure

[0.00485Amonochromaticbeamoflightisabsorbedbyacollectionofground-statehydrogenatomsinsuchawaythatsixdifferentwavelengthsareobservedwhenthehydrogenrelaxesbacktothegroundstate.Whatisthewavelengthofthebeam?[97.5Theresolvingpowerofamicroscopedependsonthewavelengthused.Ifonewishestoobserveanatom,aresolutionofapproximay1.0010-11mwouldberequired.(a)Ifelectronsareused(inanelectronmicroscope),whatminimumkicenergyisrequiredfortheelectrons?(b)Ifphotonsareusedasinanopticalmicroscope,whatminimumphotonenergyisrequired?[15.1keV;124Anelectron(me=9.11031kg)andabullet(m=0.020kg)eachhaveaspeedof500m/s,accuratetowithin0.010%.Withinwhatlimitscouldwedetermhepositionsoftheobjects?[Within1.16mmfortheelectron,5.31032mforthe(a)A electronhasawavefunctionxAei5001010x,wherexisinmeters. itsdeBrogliewavelength,( itsmomentum,( itskicenergyinelectron(b)Thewavefunctionforaparticleisx fora>0and–∞<x+∞.Determ heprobabilitythattheparticleislocatedsomewher weenx=–aandx=+a.[1.2610-10m,5.2710-24kgm/s,95.5eV,Aphotonwithwavelengthλisabsorbedbyanelectronconfinedtoabox.Asaresult,theelectronmovesfromstaten=1ton=4.Findthelengthoftheboxasafunctionof Whatisthewavelengthofthephotonemittedinthetransitionofthaectronfromthestaten=4tothestaten=2?[L=(15hλ/8mec)1/2,1.25EE100211（12λA（1），λ’Bλ方向移動(dòng)，如圖1所示。確定Δλ=λ”–λ的數(shù)值。1.00.10-11m15.1keV；電子（me=9.1.10.31kg）和子彈（m=0.020kg）500m/s0.010%1.16mm5.3.10.32m5.001010x(a)自由電子的波函數(shù)為..x..Aei，其中x的單位為米。求(i)其德波長(zhǎng) i)其動(dòng)能