Eigen Energy Solver for Schroedinger Equation

Finds eigen energies for nearly any potential and resulting Schroedinger equation MATLAB can handle.

The program 'Efinder' numerically solves the Schroedinger equation using MATLAB's 'ode45' within a range of energy values. By taking advantage of the dramatic endpoint behavior of the resulting wave solutions, 'Efinder' determines the eigen energies to any accuracy needed.

This program has been used to determine the eigen energies for several potentials, one of which being that for a fluxon trapped in a double-
well potential. The Schroedinger equation for this type of potential must be solved numerically, as no substitutions or other method has yet been devised that can solve this type of differential equation to yield a formulaic solution for En.

Inside the zip file, three files were included and the instructions to and descriptions of the files have been written into each one individually:

The 'Efinder' program has been written to allow the user to simply input their particular potential into the the program and then specify the various parameters as they feel fit;

The program 'EfinderProof' uses a potential in the Schroedinger equation that can be solved to yield a formulaic solution for En and so compares the values of eigen energies found using this program to the actual values as a means to prove the validity of this program and demonstrate the programs accuracy;

The program 'Efinderimbedded', much like its name suggests, is an example of the program Efinder being imbedded in several for loops.