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

Abstract

In the framework of the position-dependent mass quantum mechanics, the three dimensional Schrödinger equation is studied by applying the Laplace transforms combining with the point canonical transforms. For the potential analogues to Morse potential and via the Pekeris approximation, we introduce the general solutions appropriate for any kind of position dependent mass profile which obeys a key condition. For a specific position-dependent mass profile, the bound state solutions are obtained through an analytical form. The constant mass solutions are also relived.

Energy eigenvalues and finite-temperature magnetization for the improved Scarf II potential in the presence of external magnetic and Aharonov-Bohm flux fields

“…Some of the proposed methods include; the functional analysis approach, supersymmetric quantum mechanics approach, Laplace transform method, asymptotic iteration method and so on. Utilizing these methods, the exact and approximate analytical solutions of the Schrödinger equation (SE) have been obtained using different potential functions based on the Pekeris and Greene-Aldrich approximation schemes [ [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] ].…”