Sobre a introdução de um operador de translação generalizado na mecânica quântica não-relativística

Abstract

In this work we analyze some aspects related to the introduction, in the non-relativistic quantum mechanics,of a translation operator whose action is a function of the point of application. From the introduction of this operator, we derive a modified canonical commutation relation and a modified representation for the momentum operator and we show that such changes require a restructuring of the Hilbert space. We also see that the “new” Hilbert space can be associated with the case of a particle with position dependent mass and also that of a particle moving in a curved space. Still, we compare our formalism with the formalism of von Roos, we analyze the classical limit of this formalism,we solve the problem of a particle with position-dependent mass in two dimensions and we end up analyzing some quantities of information theory for the case of a one-dimensional harmonic particle.