Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

DOI10.1063/1.5017809zbMath1386.81069arXiv1712.00329OpenAlexW2774080092MaRDI QIDQ4639357

Christiane Quesne

Publication date: 9 May 2018

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

Full work available at URL: https://arxiv.org/abs/1712.00329

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) Supersymmetry and quantum mechanics (81Q60) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (3)

Comment on ‘Two-dimensional position-dependent massive particles in the presence of magnetic fields’ ⋮ Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere ⋮ On the classical and quantum dynamics of a class of nonpolynomial oscillators

Cites Work

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• One-dimensional quasi-exactly solvable Schrödinger equations
• One-dimensional model of a quantum nonlinear harmonic oscillator
• A quantum exactly solvable nonlinear oscillator with quasi-harmonic behaviour
• An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates
• Prepotential approach to exact and quasi-exact solvabilities
• Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
• Quasi-exactly-solvable problems and sl(2) algebra
• Methods for generating quasi-exactly solvable potentials
• Quasi-exactly solvable potentials with two known eigenstates
• The quantum harmonic oscillator on the sphere and the hyperbolic plane
• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• ON QUASI-EXACTLY SOLVABLE PROBLEMS AND SUPERSYMMETRY
• Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates
• Quantum oscillator and Kepler–Coulomb problems in curved spaces: Deformed shape invariance, point canonical transformations, and rational extensions
• Curvature-dependent formalism, Schrödinger equation and energy levels for the harmonic oscillator on three-dimensional spherical and hyperbolic spaces
• Special function solutions of a spectral problem for a nonlinear quantum oscillator
• Exact polynomial solutions of second order differential equations and their applications
• Energy eigenvalues of a quantum anharmonic oscillator from supersymmetry: the concept of conditional shape-invariance symmetry
• Quasi-exactly solvable potentials with three known eigenstates
• A non-linear oscillator with quasi-harmonic behaviour: two- andn-dimensional oscillators
• Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
• On a unique nonlinear oscillator
• Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem
• Extended Krein-Adler theorem for the translationally shape invariant potentials
• Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces

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