Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions

DOI10.1063/1.4801812zbMath1281.81033OpenAlexW2062633461MaRDI QIDQ5397819

Christopher R. Gordon, Axel Schulze-Halberg

Publication date: 24 February 2014

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

Full work available at URL: https://doi.org/10.1063/1.4801812

Mathematics Subject Classification ID

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)

Cites Work

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• The quantum harmonic oscillator on the sphere and the hyperbolic plane
• Discrete spectra for confined and unconfined −a/r + br2 potentials in d-dimensions
• Special function solutions of a spectral problem for a nonlinear quantum oscillator
• Energy eigenvalues and Einstein coefficients for the one-dimensional confined harmonic oscillators
• A generalized quantum nonlinear oscillator
• A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator

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