Time-independent approximations for time-dependent optical potentials
Department of Mathematics, City, University of London, Northampton Square, London, EC1V 0HB, UK
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Accepted: 29 November 2019
Published online: 28 January 2020
We explore the possibility of modifying the Lewis–Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed, but the subsequently resulting time-independent eigenvalue system is not solvable exactly. We propose to carry out this step in an approximate fashion, such as employing standard time-independent perturbation theory or the WKB approximation, and subsequently feeding the resulting approximated expressions back into the time-dependent scheme. We illustrate the quality of this approach by contrasting an exactly solvable solution to one obtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potentials.
© The Author(s), 2020