Eliminating the Second-Order Time Dependence from the Time Dependent Schr\"{o}dinger Equation Using Recursive Fourier Transforms
Abstract
A strategy is developed for writing the time-dependent Schr\"{o}dinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics.
Keywords
Cite
@article{arxiv.2306.03107,
title = {Eliminating the Second-Order Time Dependence from the Time Dependent Schr\"{o}dinger Equation Using Recursive Fourier Transforms},
author = {Sky Nelson-Isaacs},
journal= {arXiv preprint arXiv:2306.03107},
year = {2024}
}
Comments
28 pages,10 figures. Revision: minor modification of title. Inserted additional discussion on four-wave mixing. Revision: minor notational clarifications and corrections. Revision: title updated per reviewer suggestions. Figures improved for clarity. Minor adjustments to ordering of sections