Quantum integrals of motion for variable quadratic Hamiltonians

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.02.020· OSTI ID:21452999

Cordero-Soto, Ricardo ^[1]; Suazo, Erwin ^[2]

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1. Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)
2. Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico)

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

• OSTI ID: 21452999
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 9; Other Information: DOI: 10.1016/j.aop.2010.02.020; PII: S0003-4916(10)00052-7; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
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HAMILTONIANS
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OSCILLATORS
PROPAGATOR
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SCHROEDINGER EQUATION
TIME DEPENDENCE
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
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EQUIPMENT
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PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
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