Canonical transforms. IV. Hyperbolic transforms: Continuous series of SL(2,R) representations

DOI10.1063/1.524486zbMath0449.44004OpenAlexW2031954932MaRDI QIDQ3896013

Kurt Bernardo Wolf

Publication date: 1980

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

Full work available at URL: https://semanticscholar.org/paper/f8ea6d332055cddf2aa13428a7a35eaa394d6ae0

zbMATH Keywords

Schrödinger HamiltoniansBargmann realizationkernel involving Hankel and Macdonald functionsLie algebra of second-order differential operators

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Applications of Lie groups to the sciences; explicit representations (22E70) Ordinary differential operators (34L99)

Related Items (5)

The Gel’fand realization and the exceptional representations of SL(2,R) ⋮ Development of Linear Canonical Transforms: A Historical Sketch ⋮ The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis ⋮ Invariant inner products on spaces of solutions of the Klein–Gordon and Helmholtz equations ⋮ The unitary irreducible representations of SL(2, R) in all subgroup reductions

Cites Work

• Canonical transformations to action and angle variables and their representations in quantum mechanics
• The Plancherel formula for the universal covering group of SL(R, 2)
• Canonical transforms. I. Complex linear transforms
• Canonical transforms. II. Complex radial transforms
• Canonical transforms. III. Configuration and phase descriptions of quantum systems possessing an s l (2,R) dynamical algebra
• Canonical transforms, separation of variables, and similarity solutions for a class of parabolic differential equations
• On self-reciprocal functions under a class of integral transforms
• The Lorentz group in the oscillator realization. I. The group SO(2,1) and the transformation matrices connecting the SO(2) and SO(1,1) bases
• Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I
• Group Representation in a Continuous Basis: An Example
• Linear Canonical Transformations and Their Unitary Representations
• New forms for the representations of the three-dimensional Lorentz group
• Canonical Transformations and Quantum Mechanics

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