Quantum integrals of motion for variable quadratic Hamiltonians

Ricardo Cordero-Soto; Erwin Suazo; Sergei Suslov

doi:10.1016/j.aop.2010.02.020

Quantum integrals of motion for variable quadratic Hamiltonians

Ricardo Cordero-Soto, Erwin Suazo, Sergei Suslov

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger 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.

Original language	English (US)
Pages (from-to)	1884-1912
Number of pages	29
Journal	Annals of Physics
Volume	325
Issue number	9
DOIs	https://doi.org/10.1016/j.aop.2010.02.020
State	Published - Sep 2010

Keywords

Caldirola-Kanai Hamiltonians
Cauchy initial value problem
Ehrenfest's theorem
Ermakov's equation
Green function
Lewis-Riesenfeld dynamical invariant
Propagator
Quantum damped oscillators
Quantum integrals of motion
The time-dependent Schrödinger equation

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.aop.2010.02.020

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title = "Quantum integrals of motion for variable quadratic Hamiltonians",

abstract = "We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schr{\"o}dinger 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.",

keywords = "Caldirola-Kanai Hamiltonians, Cauchy initial value problem, Ehrenfest's theorem, Ermakov's equation, Green function, Lewis-Riesenfeld dynamical invariant, Propagator, Quantum damped oscillators, Quantum integrals of motion, The time-dependent Schr{\"o}dinger equation",

author = "Ricardo Cordero-Soto and Erwin Suazo and Sergei Suslov",

year = "2010",

month = sep,

doi = "10.1016/j.aop.2010.02.020",

language = "English (US)",

volume = "325",

pages = "1884--1912",

journal = "Annals of Physics",

issn = "0003-4916",

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TY - JOUR

T1 - Quantum integrals of motion for variable quadratic Hamiltonians

AU - Cordero-Soto, Ricardo

AU - Suazo, Erwin

AU - Suslov, Sergei

PY - 2010/9

Y1 - 2010/9

N2 - We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger 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.

AB - We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger 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.

KW - Caldirola-Kanai Hamiltonians

KW - Cauchy initial value problem

KW - Ehrenfest's theorem

KW - Ermakov's equation

KW - Green function

KW - Lewis-Riesenfeld dynamical invariant

KW - Propagator

KW - Quantum damped oscillators

KW - Quantum integrals of motion

KW - The time-dependent Schrödinger equation

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U2 - 10.1016/j.aop.2010.02.020

DO - 10.1016/j.aop.2010.02.020

M3 - Article

AN - SCOPUS:77956393369

SN - 0003-4916

VL - 325

SP - 1884

EP - 1912

JO - Annals of Physics

JF - Annals of Physics

IS - 9

ER -

Quantum integrals of motion for variable quadratic Hamiltonians

Abstract

Keywords

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