### 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 | |

State | Published - Sep 2010 |

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### 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

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*325*(9), 1884-1912. https://doi.org/10.1016/j.aop.2010.02.020

**Quantum integrals of motion for variable quadratic Hamiltonians.** / Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 325, no. 9, pp. 1884-1912. https://doi.org/10.1016/j.aop.2010.02.020

}

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

UR - http://www.scopus.com/inward/record.url?scp=77956393369&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956393369&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2010.02.020

DO - 10.1016/j.aop.2010.02.020

M3 - Article

AN - SCOPUS:77956393369

VL - 325

SP - 1884

EP - 1912

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 9

ER -