New quasi-exactly solvable Hamiltonians in two dimensions

DOI10.1007/BF02099982zbMath0811.35106MaRDI QIDQ1317404

Artemio González-López, Niky Kamran, Peter J. Olver

Publication date: 24 March 1994

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

zbMATH Keywords

Lie algebrasquasi-exactly solvable Hamiltoniansquasi-exactly solvable operators

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (14)

SOLVABILITY OF THE G₂ INTEGRABLE SYSTEM ⋮ Two-body Coulomb problem and \(g^{(2)}\) algebra (once again about the hydrogen atom) ⋮ On the construction of quasi-exactly solvable Schrödinger operators on homogeneous spaces ⋮ \(\mathfrak{sl}(M+1)\) construction of quasi-solvable quantum \(M\)-body systems. ⋮ Connection between \(q\)-deformed anharmonic oscillators and quasi-exactly soluble potentials ⋮ Turbiner's conjecture in three dimensions ⋮ A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type ⋮ New spin Calogero-Sutherland models related to \(B_N\)-type Dunkl operators ⋮ Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators ⋮ The Lie algebraic structure of differential operators admitting invariant spaces of polynomials ⋮ Quasi-exactly solvable \(2\times 2\) matrix Schrödinger models ⋮ The multidimensional Darboux transformation ⋮ Inhomogeneous XX spin chains and quasi-exactly solvable models ⋮ Algebraic exact solvability of trigonometric-type Hamiltonians associated to root systems

Cites Work

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• Lie algebras of differential operators and Lie-algebraic potentials
• Group theory approach to scattering
• Quantal problems with partial algebraization of the spectrum
• Group theory approach to scattering. II: The Euclidean connection
• Quasi-exactly-solvable problems and sl(2) algebra
• Equivalence of Differential Operators
• QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES
• Quasi-exactly solvable Lie algebras of differential operators in two complex variables
• On polynomial solutions of differential equations
• Lie Algebras of Differential Operators in Two Complex Variables

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