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 ${\hat{p}}_q$, and its canonically conjugate deformed position operator ${\hat{x}}_q$. 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.

5 pages, 4 figures (12 eps files)

References in corpus (4)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
• Quantum Confinement in Nonadditive Space with a Spatially Dependent Effective Mass for Si and Ge Quantum Wells
• Role of Quantum Confinement in Luminescence Efficiency of Group IV Nanostructures

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