A split kinetic energy solution scheme applied to various delta potentials in quantum mechanical systems

Abstract

In this work, we extend the split previously developed kinetic energy (dubbed as KEP) method Mineo and Chao (2012) by modifying the mass parameter to include the mass. We first show how to separate the total system into the subsystems with 3 attractive delta potentials by using the KEP method. For repulsive delta potentials, we introduce negative mass terms. Two cases are demonstrated using the negative mass terms for repulsive delta potential problems in quantum mechanics. Our work shows that the KEP solution scheme can be used to obtain not only the exact energies but also the exact wavefuctions very precisely.