mathematica for Quantum mechanics.PDF

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1、5QuantumMechanics5.1IntroductionQuantummechanicscomparedwithmechanicsisaveryyoungtheory.Thetheoryemergedat1900whenMaxPlanck(seeFigure5.1.1)examinedtheblackbodyradiationinthermodynamics.ThediscoverybyPlanckwasthattheblackbodyradiationcanbedescribedbyaunifiedrelationinterpolatin

2、gbetweenthehigh-frequencylimitproposedbyWienandthelow-frequencylimitfavoredbyRayleigh.ThemajorassumptionbyPlanckwasthattheenergyinthisrelationislinearinfrequencyanddiscreteHE=ÑwL.Planckbelievedthatthisquantizationappliedonlytotheabsorptionandemissionofenergybymatter,nottoelect

3、romagneticwavesthemselves.However,itturnedouttobemuchmoregeneralthanhecouldhaveimagined.5885.1IntroductionFigure5.1.1.MaxPlanck:bornApril23,1858;diedOctober4,1947.AnotheranchormaninquantummechanicswasErwinSchrödinger(seeFigure5.1.2)whoinventedwavemechanicsin1926.Readingthethes

4、isofLouisdeBroglie,hewasinspiredtowritedownawaveequationwhichestablishedasecondapproachtomathematicallydescribequantummechanics.Figure5.1.2.ErwinSchrödinger:bornAugust12,1887;diedJanuary4,1961.5.QuantumMechanics589ItwasWernerHeisenberg(seeFigure5.1.3)whofirstgaveasounddescript

5、ionofquantummechanicswithhismatrixmechanicsin1925.Heisenbergwasstudyingasetofquantizedprobabilityamplitudeswhenheusedamatrixalgebra.Theseamplitudesformedanoncommutativealgebra.ItwasMaxBornandJordaninGöttingenwhorecognizedthisnoncommutativealgebratobeamatrixalgebra.Anotherfunda

6、mentalachievementbyHeisenbergin1927wastheuncertaintyprinciplewhichgovernsallquantummechanicalsystems.Figure5.1.3.WernerHeisenberg:bornDecember5,1901;diedFebruary1,1976.Today,quantummechanicsisacentraltheoryinphysicstodescribemicroandnanophenomenainatomicsystemsorsemiconductors

7、,forexample.Quantummechanicsinitsfield-theoreticextensionsisimportantindiscussionsoftheunificationoffundamentalforces.Theapplicationofquantummechanicsrangesfromnanosystemsuptolarge-scalesystemssuchasblackholes.Quantummechanicsis,intermsofitsapplication,bynomeansaself-contained

8、theory.Themajoropenquestioninquantumtheoryistheunificationwit