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Title: Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states

Abstract

Using the transformations from paper I, we show that the Schroedinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated. (c) 2000 American Institute of Physics.

Authors:
 [1];  [2]
  1. Theoretical Division (MS-B285), Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545 (United States)
  2. Department of Chemistry, University of Calgary, Calgary, Alberta T2N 1N4, (Canada)
Publication Date:
OSTI Identifier:
20216306
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 41; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCHROEDINGER EQUATION; SYMMETRY GROUPS; ALGEBRA; TRANSFORMATIONS; HAMILTONIANS; LIE GROUPS; THEORETICAL DATA

Citation Formats

Nieto, Michael Martin, and Truax, D. Rodney. Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states. United States: N. p., 2000. Web. doi:10.1063/1.533269.
Nieto, Michael Martin, & Truax, D. Rodney. Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states. United States. doi:10.1063/1.533269.
Nieto, Michael Martin, and Truax, D. Rodney. Mon . "Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states". United States. doi:10.1063/1.533269.
@article{osti_20216306,
title = {Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states},
author = {Nieto, Michael Martin and Truax, D. Rodney},
abstractNote = {Using the transformations from paper I, we show that the Schroedinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated. (c) 2000 American Institute of Physics.},
doi = {10.1063/1.533269},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 5,
volume = 41,
place = {United States},
year = {2000},
month = {5}
}