Matrix Numerov method for solving Schrödinger’s equation

 

Mohandas Pillai, Joshua Goglio, and Thad G. Walker

(Received 16 May 2012; accepted 15 August 2012)

 

 

We recast the well-known Numerov method for solving Schrodinger’s equation into a representation of the kinetic energy operator on a discrete lattice. With just a few lines of code in a high-level programming environment such asMATHEMATICA, it is simple to calculate and plot accurate eigenvalues and eigenvectors for a variety of potential problems. We illustrate the method by

calculating high-accuracy solutions for the  potential.

 

https://pages.physics.wisc.edu/~tgwalker/106.Numerov.pdf