A Path Integral Treatment of a System With Variable Mass

The propagator related to a system described by an Hamiltonien having the symetric form Ĥ=141mx̂,tp̂2+p̂21mx̂,t+Vx̂,t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat {H}=\frac {1}{4}\left (\frac {1}{m\left (\hat {x},t\right ) }\hat {p}^{2}+\hat {p}^{2}\frac {1}{m\left (\hat {x},t\right ) }\right ) +V\left (\hat {x},t\right )$\end{document}, is determined by using the path integral approach. As applications, two cases, where the mass and the potential are both dependent on time and position, are considered: a free particle with a variable massand a generalized oscillator.