Group approach to the factorization of the radial oscillator equation

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Annals of Physics (New York)

OSTI ID:450178

David, J; Fernandez, C ^[1]; Negro, J; del Olmo, M A ^[2]

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1. Departamento de Fisica, CINVESTAV, A.P. 14-740, 07000 Mexico D.F. (Mexico)
2. Departamento de Fisica Teorica, Universidad de Valladolid, E-47011 Valladolid (Spain)

This work studies a variety of factorizations for the radial isotropic oscillator Hamiltonian leading to a hierarchy of radial Hamiltonians labeled by a discrete index. These results are applied to find a relationship between the ladder operators (which allow one to move in the eigenfunction space of a fixed Hamiltonian) and shift operators (that connect eigenfunctions of different Hamiltonians inside the factorization hierarchy). The operators appearing in the factorizations span a dynamical algebra whose action is schematically drawn on a two-dimensional lattice. Afterwards it is shown in detail that the relevant subalgebra is isomorphic to an extended (1+2) Newton{endash}Hooke conformal algebra corresponding to a two-dimensional wave equation. As a byproduct, for each element of the hierarchy there is derived a new one-parametric continuous family of almost-isospectral radial Hamiltonians. Copyright {copyright} 1996 Academic Press, Inc.

• OSTI ID: 450178
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 252; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
GROUP THEORY
HAMILTONIANS
HARMONIC OSCILLATORS
MATHEMATICAL OPERATORS
QUANTUM MECHANICS
WAVE EQUATIONS
WAVE FUNCTIONS