mathematic求解薛定谔方程程序.doc

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1、个人收集整理勿做商业用途5.编程求解薛定谔方程：BeginPackage["QuantumWell`"]Clear[PsiSym,PsiASym,Spectrum］PsiSym：：usage="PsiSym[x_,k,a]determinesthesymmetriceigenfunctionforapotentialwellofdepth—V0.Theinputparameterkfixestheenergyand2athewidthofthewell。Psisymisusefulforanumericalrepresentatio

2、nofeigenfunctions。”PsiASym：：usage=”PsiASym[x_，k_，a_]determinestheantisymmetriceigenfunctionforapotentialwellofdepth—V0。Theinputparameterkfixestheenergyand2athewidthofthewell.PsiASymisusefulforanumericalrepresentationofeigenfunctions."Spectrum:：usage=”Spectrum[V0_，a_］ca

3、lculatesthenegativeeigenvaluesinapotentialwell.V0isthepotentialdepthand2athewidthofthewell.Theeigenvaluesarereturendasalistandareavailableinthevariableslsymandlasymasreplacementrules.ThecorrespondingplotsofeigenfunctionsarestoredinthevariablesPlsymandPlasym.Thedetermin

4、ingequationfortheeieenvaluesisplotted."（*—一defineglobalvariables-一*）Plsym：：usage=”Variablescontainingthesymmetricplotsoftheeigenfunctions."Plasym:：usage="Variablescontainingtheantisymmetricplotsoftheeigenfunctions。"lsym::usage=”Listofsymmetriceigenvalues。"lasym::usage=

5、”Listofantisymmetriceigenvalues.”k::usage=”Eigenvalue。”Begin[”`Private`"](＊一symmetriceigenfunctions一*）Psisym［x,k,a］:=Module[｛kapa,Al］｝,Kapa=kTan［ka];(*一normalizationconstant一＊)A1=1/Sqrt[aExp［-2akapa]（1+1/（kapaa)+kapa/（k^2a)+Kapa^2/k^2）];（＊一definethethreedomainsofsoluti

6、on一一*)Which［—Infinity

7、a/(k^2a)+Kapa^2/k^2)］;（*一definethethreedomainsofsolution一*)Which[-Infinity

8、=1，m=1,ymax,C2，rhs,lhssym,lhsasym，equatsym，equatasym，kmax，nsym，nasym,resultsym，resultasym}，（＊一defineconstantsandtheei