A new boson realization for the isotropic three-dimensional oscillator

Journal Article · Tue Sep 01 04:00:00 EDT 1992 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529567· OSTI ID:7262225

Marshalek, E R ^[1]

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1. Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 (United States)

Two new closely related boson realizations of the Heisenberg--Weyl algebra are derived that are directly equivalent to the introduction of spherical coordinates for the isotropic three-dimensional harmonic oscillator. This provides another way to obtain matrix elements of all physical operators connecting angular-momentum eigenstates, which are represented here by simple products of boson operators acting on the vacuum. Two of these bosons carry the angular-momentum quantum numbers while the third is a novel radial boson.'' In this approach, one begins by finding the nonunitary Dyson and then the unitarized Holstein--Primakoff realizations for the spectrum-generating SU(1,1){times}SO(3) algebra of the oscillator. The corresponding mappings of the Heisenberg--Weyl generators are then obtained from their tensor properties under SU(1,1){times}SO(3). The Dyson map of the Heisenberg--Weyl generators is not uniquely determined in this way, but the Holstein--Primakoff map is nevertheless unique. The possibility exists for generalization to isotropic oscillators of higher dimension, which are of interest in connection with nuclear collective motion.

• DOE Contract Number: FG02-91ER40640
• OSTI ID: 7262225
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 33:9; ISSN 0022-2488; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM OPERATORS
ANNIHILATION OPERATORS
BOSONS
CREATION OPERATORS
ELECTRONIC EQUIPMENT
EQUIPMENT
HARMONIC OSCILLATORS
LIE GROUPS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
OSCILLATORS
QUANTUM OPERATORS
SO GROUPS
SO-3 GROUPS
SU GROUPS
SYMMETRY GROUPS
UNITARITY