City Research Online

Abstract

We explore the possibility of modifying the Lewis-Riesenfeld method ofin-variants developed originally to find exact solutions for time-dependent quantum me-chanical systems for the situation in which an exact invariant can beconstructed, butthe subsequently resulting time-independent eigenvalue system is not solvable exactly.We propose to carry out this step in an approximate fashion, such as employing stan-dard time-independent perturbation theory or the WKB approximation, and subsequentlyfeeding the resulting approximated expressions back into the time-dependent scheme. Weillustrate the quality of this approach by contrasting an exactly solvable solution to oneobtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potentials

Publication Type:	Article
Additional Information:	© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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