The Time Inversion for Modified Oscillators
Abstract
We discuss a new completely integrable case of the time-dependent Schroedinger equation in with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator recently considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is also found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. Particular solutions of the corresponding Schroedinger equations are also obtained. A Hamiltonian structure of the classical integrable problem and its quantization are also discussed.
Keywords
Cite
@article{arxiv.0808.3149,
title = {The Time Inversion for Modified Oscillators},
author = {Ricardo Cordero-Soto and Sergei K. Suslov},
journal= {arXiv preprint arXiv:0808.3149},
year = {2009}
}
Comments
33 pages, four figures, and two tables