The coordinate transformation and the exact solutions of the Schrödinger equation with position-dependent effective mass
Guo-Xing Ju, Chang-Ying Cai, Yang Xiang, Zhong-Zhou Ren
Abstract
Using the coordinate transformation method, we solve the one-dimensional Schrödinger equation with position-dependent mass(PDM). The explicit expressions for the potentials, energy eigenvalues and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hemite and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm which produced from the dependence of mass on the coordinate, compared with that for the systems of constant mass. The properties of Vm for several mass functions are discussed.
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