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 Schrödinger equations with constant mass using point canonical transformation. The Oscillator, Coulomb, and Morse class of potentials are considered.

The Dirac equation for a charged particle in a static electromagnetic field is written for the special case of a spherically symmetric potential. Besides the well-known Dirac-Coulomb and Dirac-oscillator potentials, we obtain a relativistic version of the $S$-wave Morse potential. This is accomplished by adding a simple exponential potential term to the Dirac operator, which in the nonrelativistic limit reproduces the usual Morse potential. The relativistic bound-states spectrum and spinor wave functions are obtained.