Exactly solvable effective mass Schrödinger equation with coulomb-like potential

Exactly solvable Schrödinger equation (SE) with a position-dependent mass distribution allowing Morse-like eigenvalues is presented. For this, the position-dependent mass Schrödinger equation is transformed into a standard SE, with constant mass, by means of the point canonical transformation scheme. In that method, the choice of potential for the position-dependent mass Schrödinger equation allows us to obtain the transformation that should be used to find the exactly solvable SE. As a useful application of the proposal, the equivalent of the Witten superpotential is chosen to be constant to find the position-dependent mass distribution and the exactly solvable potential V(m(x)) allowing Morse-type energy spectra. This V(m(x)) is shown to have a Coulomb potential structure and can be useful in the study of the electronic properties of materials in which the carrier effective mass depends on the position. Moreover, the worked example, the approach is general and can be applied in the search of new potentials suitable on the study of quantum chemical systems.