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

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