Coherent states for general potentials. I. Formalism

Journal Article · Sat Sep 15 00:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.1321· OSTI ID:5752638

Nieto, M M; Simmons, Jr, L M

We first review the properties of the harmonic-oscillator coherent states which can be equivalently defined as (a) a specific subset of the x-p minimum-uncertainty states, (b) eigenstates of the annihilation operator, or (c) states created by a certain unitary exponential displacement operator. These definitions are not equivalent in general. Then we present a new method for finding coherent states for particles in general potentials. Its basis is the desire to find those states which most nearly follow the classical motion, but it is most nearly a generalization of the minimum-uncertainty method. The properties of these states are discussed in detail. Next we show that the annihilation operator and displacement operator methods, as heretofore defined, cannot be applied to general potentials (whose eigenvalues are not equally spaced). We define a generalization of these methods but show that the states so defined are not, in general, equivalent to the minimum-uncertainty coherent states. We discuss a number of properties of our coherent states and the procedures we have used.

• Research Organization: Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 5752638
• Journal Information: Phys. Rev., D; (United States), Vol. 20:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HARMONIC OSCILLATORS
EIGENSTATES
ANNIHILATION
CLASSICAL MECHANICS
EIGENVALUES
QUANTUM FIELD THEORY
SCHROEDINGER EQUATION
UNCERTAINTY PRINCIPLE
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC INTERACTIONS
EQUATIONS
FIELD THEORIES
INTERACTIONS
MECHANICS
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics