Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries
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Publication:3441648
DOI10.1063/1.2174237zbMath1111.81086OpenAlexW2171338931MaRDI QIDQ3441648
George S. Pogosyan, Willard jun. Miller, Ernest G. Kalnins
Publication date: 16 May 2007
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://hdl.handle.net/10289/1175
PDEs in connection with quantum mechanics (35Q40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exactly and quasi-solvable systems arising in quantum theory (81U15) Groups and algebras in quantum theory and relations with integrable systems (81R12)
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Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems ⋮ Exact and quasiexact solvability of second order superintegrable quantum systems. II. Relation to separation of variables ⋮ The quantum harmonic oscillator on the sphere and the hyperbolic plane ⋮ Elliptic basis for the Zernike system: Heun function solutions ⋮ Separation equations for 2D superintegrable systems on constant curvature spaces ⋮ Quantum superintegrable systems with quadratic integrals on a two dimensional manifold ⋮ Convergence and applications of some solutions of the confluent Heun equation ⋮ On some polynomial potentials in d-dimensions ⋮ A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole ⋮ Spherical geometry, Zernike’s separability, and interbasis expansion coefficients ⋮ Solutions of two-mode bosonic and transformed Hamiltonians ⋮ Solutions for confluent and double-confluent Heun equations ⋮ Zernike System Stems from Free Motion on the 3-Sphere ⋮ The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach ⋮ Dynamical symmetry algebras of two superintegrable two-dimensional systems
Cites Work
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- General properties of potentials for which the Schrödinger equation can be solved by means of hypergeometric functions
- Continued fractions with applications
- Multiparameter spectral theory in Hilbert space
- Methods of calculation in quantum theory. Elementary quantum mechanics: represented by problems and solutions
- Quasi-exactly-solvable problems and sl(2) algebra
- Superintegrable systems: Polynomial algebras and quasi-exactly solvable Hamiltonians
- Completeness of superintegrability in two-dimensional constant-curvature spaces
- Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems
- Exact solvability of superintegrable systems
- FRACTIONAL STATISTICS IN ONE DIMENSION: MODELING BY MEANS OF 1/x2 INTERACTION AND STATISTICAL MECHANICS
- Wave Functions for the Hydrogen Atom in Spheroidal Coordinates I: The Derivation and Properties of the Functions
- Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory
- Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform
- Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory
- Path integral treatment of the hydrogen atom in a curved space of constant curvature. II. Hyperbolic space
- Perturbative quantum corrections and flux compactifications
- Path integral treatment of the hydrogen atom in a curved space of constant curvature
- Dynamical symmetries in a spherical geometry. I
- Dynamical symmetries in a spherical geometry. II
- On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space
- Maximal superintegrability onN-dimensional curved spaces
- Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
- Completeness of multiseparable superintegrability inE2,C
- Completeness of multiseparable superintegrability on the complex 2-sphere
- Finite two-dimensional oscillator: II. The radial model
- Quasi-exact solvability and the direct approach to invariant subspaces
- Superintegrability in three-dimensional Euclidean space
- Superintegrability on the two-dimensional hyperboloid. II
- Isochronic potentials and new family of superintegrable systems
- Spiked harmonic oscillators
- Superintegrability in a two-dimensional space of nonconstant curvature
- Quantum superintegrability and exact solvability in n dimensions
- Separation of variables and subgroup bases on n-dimensional hyperboloids
- Superintegrable systems in Darboux spaces
- Hamiltonians separable in Cartesian coordinates and third-order integrals of motion
- Problem of two Coulomb centres at large intercentre separation: asymptotic expansions from analytical solutions of the Heun equation
- Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions
- Enumeration of Potentials for Which One-Particle Schroedinger Equations Are Separable
