Path Integral Methods From the Generalized Displacement Operator, and Some of Their Applications

The non-relativistic Feynman propagator with position dependent mass (PDM) is formulated by means to introduce the generalized infinitesimal translation operator approach. Which is similar to deformed quantum mechanics based on modified commutation relations. This latter is connected to the Feynman propagator with constant-mass by adopting the coordinates transformation methods, which are α−point discretization dependent, to evaluate quantum corrections. In each application, the propagator (or the Green function) is calculated, the wave functions and their associated eigenvalues are obtained, also the curves of energies are illustrated. The limit cases are then deduced for a small parameter. (author)