The relation between polynomial deformations ofsl(2,R) and quasi-exact solvability

DOI10.1088/0305-4470/33/40/308zbMath0963.81072arXivhep-th/0005141OpenAlexW3098549000MaRDI QIDQ4523652

Nathalie Debergh

Publication date: 14 January 2001

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

Full work available at URL: https://arxiv.org/abs/hep-th/0005141

zbMATH Keywords

quasi-exact solvabilitysextic oscillatorpolynomial deformations of the Lie algebra \(sl(2,\mathbb{R})\)

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Related Items (8)

Non-standard quantum algebras and finite dimensional PT -symmetric systems ⋮ Boson realizations of the polynomial angular momentum algebras with arbitrary powers and their unitarization ⋮ Differential realizations of polynomial algebras in finite-dimensional spaces of monomials. ⋮ Second harmonic Hamiltonian: algebraic and Schrödinger approaches ⋮ POLYNOMIAL DEFORMATIONS OF sl(2, ℝ) IN A THREE-DIMENSIONAL INVARIANT SUBSPACE OF MONOMIALS ⋮ Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials ⋮ Approach of spherical harmonics to the representation of the deformed su(1,1) algebra ⋮ APPROACH OF THE AZIMUTHAL AND MAGNETIC QUANTUM NUMBERS l AND m TO REPRESENTATION OF A CUBIC DEFORMATION OF su(2) ALGEBRA

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