Non trivial solution to Schrödinger equation for 1-D infinite well

[MrMuscle]

TL;DR Summary

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!

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.

 

[Orodruin]

Matlab is trying to solve your setup for an arbitrary energy $E$. This will generally not have a solution but $E$ will be quantised. What you want to do is to solve the differential equation using one of the boundary conditions, leaving you one integration constant. Then you can solve the second boundary condition for the energy. This will give you the quantised energy levels.

Note that MATLAB is not the ideal for symbolic computations.

 

[MrMuscle]

Thanks for the answer! what would you suggest for symbolic calculations?
Also, do you have any suggestions about how to modify the code?

 

[Orodruin]

Personally, I would use Mathematica. Maple is also popular.