A Semi-Analytical Solution to the Schr ¨ odinger Equation with Gaussian Well

Abstract

This paper proposes a new semi-analytical solution of the Schr¨odinger equation with Gaussian well. The approach is based on the harmonic oscillator and yields both the energy and the wave function for any specific eigenstate. Furthermore, the semi-analytical solution is compared to methods found in the literature and the Split-Operator method and deemed accurate.