Schrödinger Equation with Position-Dependent Mass

Abstract

Generally speaking, the effective mass is taken as a constant in the traditional wave equations. Recently, the study of the non-relativistic equation with the position-dependent effective mass has attracted a lot of attention to many authors. This is because such systems have been found to have wide applications in various fields such as the electronic properties of the semiconductors, 3He clusters, quantum wells, wires and dots, quantum liquids, the graded alloys, semiconductor heterostructures and others. Recently, the algebraic method has also been used to study these systems. In this Chapter, we first employ a point canonical transformation to study the D-dimensional position-dependent effective mass Schrodinger equation and then carry out two typical examples such as the harmonic oscillator and Coulomb potential.