Quantization of a particle on a two-dimensional manifold of constant curvature

DOI10.1063/1.4896817zbMath1298.81095arXiv1407.0734OpenAlexW3102253454MaRDI QIDQ2928095

Paul Bracken

Publication date: 6 November 2014

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

Full work available at URL: https://arxiv.org/abs/1407.0734

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Compact Lie groups of differentiable transformations (57S15) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (1)

Free particle and isotropic harmonic oscillator on a spheroidal surface: The Higgs-like approach

Uses Software

• Maple

Cites Work

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• Quantum motion on a torus as a submanifold problem in a generalized Dirac's theory of second-class constraints
• A quantum exactly solvable nonlinear oscillator with quasi-harmonic behaviour
• Geometric quantization and quantum mechanics
• The quantum harmonic oscillator on the sphere and the hyperbolic plane
• A non-linear oscillator with quasi-harmonic behaviour: two- andn-dimensional oscillators
• On a unique nonlinear oscillator
• The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach

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