Nontrivial solution for differential equation (Schrödinger)

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Ege Gurtan
Ege Gurtan 2019-6-10
Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L)
You can see my code below. Could you please tell me where is my mistake?
Thanks in advance!
clear,clc %Solution of Schrödinger eqn with 1-D infinite well
syms WF(x) V(x) %WF is the wavefunction, V(x) is the potential
syms hbar m L E positive %E energy, L length of the well, m mass, hbar reduced planck
V(x)=0 %Potential
Sch=((-hbar^2)/(2*m))*diff(WF,x,2)+V*WF==E*WF %Schrödinger equation
Solution1=dsolve(Sch) %Solution without applying boundary conditions
%BOUNDARY CONDITIONS
cond1=WF(0)==0;
cond2=WF(L)==0;
conds=[cond1 cond2];
Solution2=dsolve(Sch,conds) %Solution with applying boundary conditions.

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