A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to image-doped semiconductors Original Research Article

We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in image-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) .