Introduction to Quantum Mechanics.pdf

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1、Chapter2IntroductiontoQuantumMechanics2-2Schrodinger’sWaveEquation為什麼要解薛丁格方程式，因為我們要知道在半導體中的電子能階。例如對於發光半導體而言，知道能階才能知道此材料要發什麼樣顏色的光。透過解薛丁格方程式把電子的機率波解出來，然後透過電子的能量運算子對機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.古典力學觀點DoubleSlitExperimentforParticlesTheabovetwo-slitpatternhappenstobesimplythesumofthepatternsforeachslitconsideredseparately:ifhalfthebulletswerefiredwithonlytheleftslitopenandthenhalfwerefiredwithjusttherightslitopen,theresultwouldbethesame.Wi

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

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

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

7、觀點：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電子機率波V)x(potentialfunction電子所處位置的位能melectronmass電子的質量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