Solutions of the nonrelativistic wave equation with position-dependent effective mass

Abstract

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation. The Oscillator, Coulomb, and Morse class of potentials are considered.

12 pages;PACS number(s): 03.65.Ca, 03.65.Ge, 03.65.Fd, 03.65.Db

References in corpus (6)

• Exact solvability of potentials with spatially dependent effective masses
• Energy spectrum of the relativistic Dirac-Morse problem
• Relativistic shape invariant potentials
• Comprehensive analysis of conditionally exactly solvable models
• Solution of the relativistic Dirac-Morse problem
• Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations

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