Solutions of Morse potential with position-dependent mass by Laplace transform

In the framework of the position-dependent massquantum mechanics, the three dimensional Schro¨dingerequation is studied by applying the Laplace transformscombining with the point canonical transforms. For thepotential analogues to Morse potential and via the Pekerisapproximation, we introduce the general solutions appropriatefor any kind of position dependent mass profilewhich obeys a key condition. For a specific position-dependentmass profile, the bound state solutions are obtainedthrough an analytical form. The constant mass solutions arealso relived.