Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

DOI10.1063/1.4905167zbMath1308.81074arXiv1411.7152OpenAlexW3099170388MaRDI QIDQ5499045

V. Chithiika Ruby, V. K. Chandrasekar, Murugaian Senthilvelan, Muthusamy Lakshmanan

Publication date: 11 February 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7152

zbMATH Keywords

quantizationgeneral Liénard type nonlinear oscillatorsHermitian orderingLie point symmetry techniqueposition-dependent mass quantum systemsquantum solvability of Hermitian Hamiltoniansolvability of non-Hermitian Hamiltonian

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Exactly and quasi-solvable systems arising in quantum theory (81U15) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (8)

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass ⋮ The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective ⋮ Lie point symmetries classification of the mixed Liénard-type equation ⋮ Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator ⋮ The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass ⋮ κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass ⋮ Bouncing and cyclic quantum primordial universes and the ordering problem ⋮ On the classical and quantum dynamics of a class of nonpolynomial oscillators

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