Quantum oscillator and Kepler–Coulomb problems in curved spaces: Deformed shape invariance, point canonical transformations, and rational extensions

DOI10.1063/1.4963726zbMath1349.81102arXiv1604.04136OpenAlexW2342222376MaRDI QIDQ2832711

Christiane Quesne

Publication date: 14 November 2016

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

Full work available at URL: https://arxiv.org/abs/1604.04136

zbMATH Keywords

deformed shape invariancenonextended and extended potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Atomic physics (81V45) Supersymmetry and quantum mechanics (81Q60) Isospectrality (58J53) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (10)

Supersymmetry and shape invariance of exceptional orthogonal polynomials ⋮ Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems ⋮ Mapping of two-dimensional Schrödinger equation under the point transformation ⋮ Superintegrability, symmetry and point particle T-duality ⋮ An efficient interpolating wavelet collocation scheme for quasi‐exactly solvable Sturm–Liouville problems in ℝ+ ⋮ Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere ⋮ Deformed shape invariance symmetry and potentials in curved space with two known eigenstates ⋮ Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces ⋮ so(2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation ⋮ 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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