Calculation of energy levels with Lennard-Jones, Hyperbolic Cosine and Morse potentials using the matrix and pairing method

Abstract

This work represents an academic exercise in which two numerical methods are compared; the matrix and matching method for the solutions to Schrödinger’s one-dimensional equation with the Lennard-Jones potential, hyperbolic cosine and Morse. With both methods, the energy levels and associated wave functions are obtained with a low error, this from the comparing between the numerically calculated energies with those of hyperbolic cosine potential which are known analytically.