### 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) |
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Pages (from-to) | 1884-1912 |

Number of pages | 29 |

Journal | Annals of Physics |

Volume | 325 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 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

- Physics and Astronomy(all)

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## Cite this

Cordero-Soto, R., Suazo, E., & Suslov, S. (2010). Quantum integrals of motion for variable quadratic Hamiltonians.

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