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arXiv · 1305.6307

Generalized space and linear momentum operators in quantum mechanics

Bruno G. da Costa·Ernesto P. Borges
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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.

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Bruno G. da Costa, Ernesto P. Borges. 2013-05-27. Generalized space and linear momentum operators in quantum mechanics. https://doi.org/10.1063/1.4884299

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