On the Lewis-Riesenfeld (Dodonov-Man'ko) invariant method
Quantum Physics
2015-03-05 v1 Mathematical Physics
math.MP
Abstract
We revise the Lewis-Riesenfeld invariant method for solving the quantum time-dependent harmonic oscillator in light of the Quantum Arnold Transformation previously introduced and its recent generalization to the Quantum Arnold-Ermakov-Pinney Transformation. We prove that both methods are equivalent and show the advantages of the Quantum Arnold-Ermakov-Pinney transformation over the Lewis-Riesenfeld invariant method. We show that, in the quantum time-dependent and damped harmonic oscillator, the invariant proposed by Dodonov & Man'ko is more suitable and provide some examples to illustrate it, focusing on the damped case.
Cite
@article{arxiv.1503.01371,
title = {On the Lewis-Riesenfeld (Dodonov-Man'ko) invariant method},
author = {Julio Guerrero and Francisco F. López-Ruiz},
journal= {arXiv preprint arXiv:1503.01371},
year = {2015}
}
Comments
19 pages. Accepted for publication in Physica Scripta