Quasi-exactly solvable potentials on the line and orthogonal polynomials

DOI10.1063/1.531591zbMath0863.58024arXivhep-th/9603103OpenAlexW3103777391MaRDI QIDQ5284834

No author found.

Publication date: 3 June 1997

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

Full work available at URL: https://arxiv.org/abs/hep-th/9603103

zbMATH Keywords

quasi-exactly solvable Hamiltonianweakly orthogonal polynomials

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items

Anti-isospectral transformations, orthogonal polynomials, and quasi-exactly solvable problems ⋮ QES SYSTEMS, INVARIANT SPACES AND POLYNOMIALS RECURSIONS ⋮ A Unifying E2-Quasi Exactly Solvable Model ⋮ On solvability and integrability of the Rabi model ⋮ Associated Lamé and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials ⋮ New classes of quasi-solvable potentials, their exactly solvable limit, and related orthogonal polynomials ⋮ \(\mathfrak{sl}(M+1)\) construction of quasi-solvable quantum \(M\)-body systems. ⋮ Do quasi-exactly solvable systems always correspond to orthogonal polynomials? ⋮ Quasiexactly solvable problems and the dual (q-)Hahn polynomials ⋮ Haydock's recursive solution of self-adjoint problems. Discrete spectrum ⋮ A QES band-structure problem in one dimension ⋮ A unified treatment of polynomial solutions and constraint polynomials of the Rabi models ⋮ The asymmetric quantum Rabi model and generalised Pöschl–Teller potentials ⋮ A new non-Hermitian \(E_2\)-quasi-exactly solvable model ⋮ A number of quasiexactly solvable N-body problems ⋮ Type A \(N\)-fold supersymmetry and generalized Bender-Dunne polynomials ⋮ Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart ⋮ Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure ⋮ Inhomogeneous XX spin chains and quasi-exactly solvable models

Cites Work

• Lie algebras of differential operators and Lie-algebraic potentials
• Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
• Quasi-exactly-solvable problems and sl(2) algebra
• Quasi-exactly solvable Lie algebras of differential operators in two complex variables
• Real Lie algebras of differential operators and quasi-exactly solvable potentials
• Quasi-exactly solvable systems and orthogonal polynomials
• Polynomial Curve Fitting with Constraint