Eliminating the Second-Order Time Dependence from the Time Dependent Schrödinger Equation Using Recursive Fourier Transforms

Abstract

A strategy is developed for writing the time-dependent Schrödinger 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.

arXiv comment28 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

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