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

• URL: http://arxiv.org/abs/2306.03107v5
• Date: Tue, 25 Jun 2024 19:21:39 GMT
• Title: Eliminating the Second-Order Time Dependence from the Time Dependent Schrödinger Equation Using Recursive Fourier Transforms
• Authors: Sky Nelson-Isaacs,
• Abstract summary: A strategy is developed for writing the time-dependent Schr"odinger Equation. The energy distribution is calculated for a number of standard theory examples at first- and second-order.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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