Lie algebras for systems with mixed spectra. I. The scattering Pöschl–Teller potential

DOI10.1063/1.526559zbMath0604.22015OpenAlexW1979047585MaRDI QIDQ3741825

Kurt Bernardo Wolf, Alejandro Frank

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1063/1.526559

zbMATH Keywords

wave functionsCasimir operatormixed spectrumPöschl-Teller Hamiltoniansp(2, \({bbfR})\) Clebsch-Gordan coefficients

Mathematics Subject Classification ID

Nuclear physics (81V35) Applications of Lie groups to the sciences; explicit representations (22E70) Lie algebras of Lie groups (22E60) Geometric quantization (53D50)

Related Items (24)

Integrable systems based on SU(p,q) homogeneous manifolds ⋮ The SU(u,v)-group path integration ⋮ Wigner functions for curved spaces. II. On spheres ⋮ The potential group approach and hypergeometric differential equations ⋮ Algebra representations on eigenfunctions of the Rosen–Morse potential ⋮ Symmetry scattering for SU(2,2) with applications ⋮ A simple difference realization of the Heisenberg q-algebra ⋮ WKB equivalent potentials for q-deformed harmonic and anharmonic oscillators ⋮ Closed expressions for matrix elements of the trigonometric Pöschl-Teller potential ⋮ Potentials derived geometrically for symmetry scattering ⋮ Path integration over compact and noncompact rotation groups ⋮ On a time-dependent extension of the Morse potential ⋮ Superintegrability on the two-dimensional hyperboloid ⋮ Temporally stable coherent states for infinite well and Pöschl–Teller potentials ⋮ Path integral treatment for a screened potential ⋮ Hidden symmetry and potential group of the Maxwell fish-eye ⋮ Superintegrability on the two-dimensional hyperboloid. II ⋮ Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters ⋮ Mutual integrability, quadratic algebras, and dynamical symmetry ⋮ Solving Simultaneously Dirac and Ricatti Equations ⋮ Orthogonal polynomials derived from the tridiagonal representation approach ⋮ Quantum mechanics inversion for symmetry scattering ⋮ Quantum phase space for the one-dimensional hydrogen atom on the hyperbola ⋮ Generalized coherent states for a relativistic model of the linear oscillator in a homogeneous external field

Cites Work

• Complex angular momenta and the groups \(\mathrm{SU}(1,1)\) and \(\mathrm{SU}(2)\)
• Irreducible unitary representations of the Lorentz group
• On the Kronecker Products of Irreducible Representations of the 2 × 2 Real Unimodular Group. I
• The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis
• The unitary irreducible representations of SL(2, R) in all subgroup reductions
• Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I
• Complete Sets of Functions on Homogeneous Spaces with Compact Stabilizers
• The Factorization Method

This page was built for publication: Lie algebras for systems with mixed spectra. I. The scattering Pöschl–Teller potential