2013/05/27 by Bruno G. da Costa, Ernesto P. Borges · 3 citations
Mathematics · Physics and Astronomy · #Banach space #Canonical coordinates #Canonical transformation #Classical mechanics #Compact operator #Complex conjugate #Finite-rank operator #Hamiltonian (control theory) #Hamiltonian mechanics #Hermitian matrix #Ladder operator #Mathematical analysis #Mathematical physics #Mathematics #Momentum operator #Operator (biology) #Phase space #Physics #Position and momentum space #Position operator #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quasinormal operator #Statistical Mechanics and Entropy #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4884299
5 pages, 4 figures (12 eps files)
arxiv created 2013/05/27 · openalex publication_date 2014/06/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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\begindocumentpq\enddocumentp̂q, and its canonically conjugate deformed position operator \documentclass[12pt]minimal\begindocumentxq\enddocumentx̂q. 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.