Introduction to Quantum Mechanics.pdf

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1、Chapter2IntroductiontoQuantumMechanics2-2Schrodinger’sWaveEquation為什麼要解薛丁格方程式，因?yàn)槲覀円涝诎雽?dǎo)體中的電子能階。例如對於發(fā)光半導(dǎo)體而言，知道能階才能知道此材料要發(fā)什麼樣顏色的光。透過解薛丁格方程式把電子的機(jī)率波解出來，然後透過電子的能量運(yùn)算子對機(jī)率波作用即可解出電子的能階。ExplanationofClassicalElectronDiffractionAgun(obeyingclassicalphysics)spraysbulletsto

2、wardsatarget.Beforetheyreachthetarget,theymustpassthroughascreenwithtwoslits.Ifbulletsgothroughtheslitstheywillmostlikelylanddirectlybehindtheslit,butiftheycomeinataslightangle,theywilllandslightlytothesides.Theresultingpatternisamapofthelikelihoodofabulletlandi

3、ngateachpoint.古典力學(xué)觀點(diǎn)DoubleSlitExperimentforParticlesTheabovetwo-slitpatternhappenstobesimplythesumofthepatternsforeachslitconsideredseparately:ifhalfthebulletswerefiredwithonlytheleftslitopenandthenhalfwerefiredwithjusttherightslitopen,theresultwouldbethesame.Wi

4、thwaves,however,theresultisverydifferent,becauseofinterference.Iftheslitswereopenedoneatatime,thepatternwouldresemblethatforbullets:twodistinctpeaks.Butwhenbothslitsareopen,thewavespassthroughbothslitsatonceandinterferewitheachother:wheretheyareinphasetheyreinfo

5、rceeachother;wheretheyareoutofphasetheycanceleachotherout.古典力學(xué)觀點(diǎn)DoubleSlitExperimentforWavesNowthequantumparadox:Electrons,likebullets,strikethetargetoneatatime.Yet,likewaves,theycreateaninterferencepattern.量子力學(xué)觀點(diǎn)：波動，粒子雙元性DoubleSlitExperimentforElectronsIfeachel

6、ectronpassesindividuallythroughoneslit,withwhatdoesit"interfere?"Althougheachelectronarrivesatthetargetatasingleplaceandtime,itseemsthateachhaspassedthrough-orsomehowfeltthepresenceofbothslitsatonce.Thus,theelectronisunderstoodintermsofawave-particleduality.量子力學(xué)

7、觀點(diǎn)：波動，粒子雙元性Illustrationof"Wave-ParticleDuality"2-2Schrodinger’sWaveEquation22???)t,x(??)t,x(??V)x(?)t,x(?j?2m2?t?x?)t,x(?wavefunctionofelectron電子機(jī)率波V)x(?potentialfunction電子所處位置的位能m?electronmass電子的質(zhì)量t?timescale,x?xscaleAssumethatthewavefunctioncanbewritteninthefo

8、rm?)t,x(??)x(?(t)帶入薛丁格方程式where?)x(isafunctionofpositionxonlyand?(t)aisfunctionoftimetonly.22???)x(??)t(??)t(?V)x(?)x(?)t(?j??)x(2m2?t?x22?1??)x(1??)t(??V)x(?j?2m?)x(2