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Decoupling the time dependent Schr\"{o}dinger equation using recursive Fourier transforms

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arXiv:2306.03107v4 Announce Type: replace
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 example 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.

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