Generalized space and linear momentum operators in quantum mechanics

Abstract

We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator \documentclass[12pt]{minimal}\begin{document}$\hat{p}_q$\end{document}p̂q, and its canonically conjugate deformed position operator \documentclass[12pt]{minimal}\begin{document}$\hat{x}_q$\end{document}x̂q. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.