Quantum-mechanical explicit solution for the confined harmonic oscillator model with the von Roos kinetic energy operator

DOI10.1016/S0034-4877(20)30055-0zbMath1451.81229OpenAlexW3081781712MaRDI QIDQ2210542

E. I. Jafarov, Sh. M. Nagiyev, A. M. Jafarova

Publication date: 7 November 2020

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(20)30055-0

zbMATH Keywords

quantum harmonic oscillatorexplicit polynomial solutionposition-dependent effective massconfined modelvon Roos kinetic energy operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (7)

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass ⋮ Effective mass of the discrete values as a hidden feature of the one-dimensional harmonic oscillator model: Exact solution of the Schrödinger equation with a mass varying by position ⋮ On two direct limits relating pseudo-Jacobi polynomials to Hermite polynomials and the pseudo-Jacobi oscillator in a homogeneous gravitational field ⋮ Quantum heat engine with level degeneracy for oscillator-shaped potential well ⋮ The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass ⋮ Angular part of the Schrödinger equation for the Hautot potential as a harmonic oscillator with a coordinate-dependent mass in a uniform gravitational field ⋮ On the classical and quantum dynamics of a class of nonpolynomial oscillators

Cites Work

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• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• On a unique nonlinear oscillator
• Dynamical Friction. I. General Considerations: the Coefficient of Dynamical Friction.

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