mathematic求解薛定谔方程程序.doc

编程求解薛定谔方程： BeginPackage[QuantumWell`] Clear[PsiSym,PsiASym,Spectrum] PsiSym::usage= PsiSym[x_ ,k ,a ] determines the symmetric eigenfunction for a potential well of depth -V0. The input parameter k fixes the energy and 2a the width of the well. Psisym is useful for a numerical representation of eigenfunctions. PsiASym::usage= PsiASym[x_ ,k_ ,a_] determines the antisymmetric eigenfunction for a potential well of depth-V0. The input parameter k fixes the energy and 2a the width of the well. PsiASym is useful for a numerical representation of eigenfunctions. Spectrum::usage=Spectrum[V0_ ,a_]calculates the negative eigenvalues in a potential well. V0 is the potential depth and 2a the width of the well.The eigenvalues are returend as a list and are available in the variables lsymand lasym as replacement rules. The corresponding plots of eigenfunctions are stored in the variables Plsym and Plasym. The determining equation for the eieenvalues is plotted. (*-一define global variables-一*) Plsym::usage= Variables containing the symmetric plots of the eigenfunctions. Plasym::usage =Variables containing the antisymmetric plots of the eigenfunctions. lsym::usage= List of symmetric eigenvalues. lasym::usage =List of antisymmetric eigenvalues. k::usage =Eigenvalue. Begin[`Private`] (*一symmetric eigenfunctions一*) Psisym[x ,k ,a ]:=Module[{kapa, Al]},Kapa = k Tan [k a]; (*一normalization constant一*) A1=1/Sqrt[a Exp[-2 a kapa] (1+1/(kapa a)+kapa/(k^2 a)+Kapa^2/k^2)]; (*一define the three domains of solution一一*) Which[-Infinityx x-a, A1 Exp[kapa x],-a=xx=a, A1 Exp[-kapa a] cos[k x]/Cos[k a], axx(Infinity, A1 Exp[-kapa x] ] ] (*---antisymmetric eigenfunctions---*) Pa iASym[x_, k_ ,a_]:=Module[{kapa, Al}, Kapa=一k Cut [k a]; (*一normalization constant一*) A1=1/Sqrt[a Exp[-2 a kapa] (1+1/(kapa a)+kapa/(k^2 a)+Kapa^2/k^2)]; (*一define the three domains of solution一*) Which[-Infinityx x-a，-Al Exp[kapa x],-a=xx‘=a, A1 Exp[-kapa a] Sin[k x]/Sin[k a],ax