Quantum Integrals of Motion for Variable Quadratic Hamiltonians
Mathematical Physics
2015-05-14 v9 math.MP
Abstract
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of 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
Cite
@article{arxiv.0912.4900,
title = {Quantum Integrals of Motion for Variable Quadratic Hamiltonians},
author = {Ricardo Cordero-Soto and Erwin Suazo and Sergei K. Suslov},
journal= {arXiv preprint arXiv:0912.4900},
year = {2015}
}
Comments
32 pages, no figures