Path integral analysis from the D-dimensional generalized displacement operator, and some of their applications

Abstract

Recently, H. Benzair et al. [Mod. Phys. Lett. A 35, 2050246 (2020).] formulated in one dimension the nonrelativistic propagator for position-dependent mass (PDM) from the generalized displacement operator approach. According to the path integral formulation, we generalize this process in [Formula: see text]-dimensional space. As a result, the wave functions are obtained analytically for the pseudo-harmonic oscillator and the inverse square plus Coulomb potentials, and the corresponding energy spectrum are studied. In addition, the effects of PDM on the canonical partition function and other thermodynamic functions have been extracted. The limit cases are then deduced for a small parameter.