Coherent states for general potentials. IV. Three-dimensional systems

Journal Article · Tue Jul 15 00:00:00 EDT 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.22.391· OSTI ID:5206024

Nieto, M M

The minimum-uncertainty coherent-states formalism is extended to higher-dimensional systems. Specifically, for spherically symmetric three-dimensional potentials the formalism looks for coherent states which are products of an angular wave function times a radial wave function. After reviewing the many studies on angular coherent states, I concentrate on the physically distinguishing radial coherent states. The radial formalism is explained in detail and contrasted with the effective one-dimensional formalism. The natural classical variables in the radial formalism are those which vary sinusoidally as g(E,L)theta(t), where theta(t) is the real azimuthal angular variable and g(E,L) is the number of oscillations between apsidal distances per classical orbit. When changed to natural quantum operators, these operators can be given as the Hermitian sums and differences of the ''l'' raising and lowering operators. The formalism is applied to the three-dimensional harmonic-oscillator and Coulomb problems.

• Research Organization: Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 5206024
• Journal Information: Phys. Rev., D; (United States), Vol. 22:2
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HARMONIC OSCILLATOR MODELS
EIGENSTATES
ANGULAR VELOCITY
CLASSICAL MECHANICS
COULOMB FIELD
EIGENFUNCTIONS
HAMILTONIANS
HYDROGEN
QUANTUM OPERATORS
THREE-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
CRYOGENIC FLUIDS
ELECTRIC FIELDS
ELEMENTS
FLUIDS
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
NONMETALS
VELOCITY
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics