Diatomic Molecules Effective Potential for an Harmonic Oscillator Model

Abstract

A model anharmonic potential was considered and was used in the Schrödinger time independent wave equation to describe a carbon monoxide molecule. Central difference scheme was used in approximating the derivative term in the Schrödinger equation leading to a tri-diagonal band system of equation. The method of LU decomposition of Gaussian – elimination with back substitution was used to solve the system because it cannot be solved analytically. The effective potentials for large α show no unique turning point but as the value of α decreases, the effective potential shows unique turning point which suggest an approach to equilibrium point.

Keywords: Anharmonic; Model; Potential; Schrödinger; Carbon monoxide; Effective potential