The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach

DOI10.1063/1.3610674zbMath1317.81128arXiv1201.5589OpenAlexW2139892480WikidataQ125587357 ScholiaQ125587357MaRDI QIDQ5266073

Mariano Santander, José F. Cariñena, Manuel F. Rañada

Publication date: 29 July 2015

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

Full work available at URL: https://arxiv.org/abs/1201.5589

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (15)

Coherent states of quantum free particle on the spherical space ⋮ Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry ⋮ $SU(2)$ -particle sigma model: momentum-space quantization of a particle on the sphere S ³ ⋮ Multipolar Hardy inequalities on Riemannian manifolds ⋮ Quantization of a particle on a two-dimensional manifold of constant curvature ⋮ Motion on constant curvature spaces and quantization using noether symmetries ⋮ Schrödinger formalism for a particle constrained to a surface in R13 ⋮ On the functions of two commuting Laplace-Beltrami operators in hyperbolic space ⋮ Coherent states on horospheric three-dimensional Lobachevsky space ⋮ Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley-Klein space and its thermodynamic properties ⋮ Free particle and isotropic harmonic oscillator on a spheroidal surface: The Higgs-like approach ⋮ Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners ⋮ The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach. II ⋮ Building a path-integral calculus: a covariant discretization approach ⋮ Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S ³ and on the hyperbolic space H ³

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