A new basis for the representations of the rotation group. Lamé and Heun polynomials

DOI10.1063/1.1666449zbMath0285.22017OpenAlexW2027009556MaRDI QIDQ4771163

Jirí Patera, Pavel Winternitz

Publication date: 1973

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

Full work available at URL: https://doi.org/10.1063/1.1666449

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (35)

HUYGENS' PRINCIPLE AND SEPARATION OF VARIABLES ⋮ Classification of the classical \(\mathrm{SL}(2,\mathbb R)\) gauge transformations in the rigid body ⋮ Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions ⋮ Representations of the quantum algebra suq(2) on a real two-dimensional sphere ⋮ Cylindrical type integrable classical systems in a magnetic field ⋮ Algebraization of difference eigenvalue equations related to \(U_q(\text{sl}_2)\) ⋮ Harmonics on hyperspheres, separation of variables and the Bethe ansatz ⋮ The four sets of additive quantum numbers of SU(3) ⋮ Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere S n and Euclidean n-space R n ⋮ Quantum superintegrability and exact solvability in n dimensions ⋮ Separation of variables and subgroup bases on n-dimensional hyperboloids ⋮ Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems ⋮ The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1) ⋮ Lie theory and separation of variables. 6. The equation i U t + Δ2U = 0 ⋮ Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials ⋮ Separation of variables in the Hamilton–Jacobi, Schrödinger, and related equations. I. Complete separation ⋮ Tridiagonalization and the Heun equation ⋮ Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group ⋮ Symmetry and separation of variables for the Helmholtz and Laplace equations ⋮ Lie theory and separation of variables. 8. Semisubgroup coordinates for Ψt t − Δ2Ψ = 0 ⋮ The Extended Rigid Body and the Pendulum Revisited ⋮ Symmetry breaking interactions for the time dependent Schrödinger equation ⋮ Lie theory and the wave equation in space–time. I. The Lorentz group ⋮ Superintegrability on the two-dimensional hyperboloid ⋮ Optimal systems and group classification of \((1+2)\)-dimensional heat equation ⋮ Symmetry and separation of variables for the Hamilton–Jacobi equation W2t−W2x −W2y =0 ⋮ Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups ⋮ The \(\text{SO}(4)\) group and the Lamé equations of the second order ⋮ Second-order supersymmetric periodic potentials ⋮ Heun operator of Lie type and the modified algebraic Bethe ansatz ⋮ Contractions of Lie algebras and separation of variables. The n-dimensional sphere ⋮ Heun algebras of Lie type ⋮ Subgroups of Lie groups and separation of variables ⋮ On the quantum inverse scattering method for the DST dimer ⋮ Lie theory and separation of variables. 4. The groups SO (2,1) and SO (3)

Cites Work

• On the general theory of collisions for particles with spin
• Angular Momentum in Sphero-Conal Coordinates

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