SCHRODINGER’S WAVE EQUATION

I am trying to simulate SCHRODINGER’S WAVE EQUATION in MATLAB,

From scratch, I am trying to obtain E(1), E(2), E(3) values. by inputing all other parameters,

What is the way to input PDE and solve the equation, I read the help page, But it is complex.

I refered

https://in.mathworks.com/help/matlab/math/partial-differential-equations.html

For reference I took Semiconductor Physics and Devices Basic Principles Fourth Edition Donald A. Neamen University of New Mexico

[KSSV]

You can solve it numerically using ode45. Read about it.