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Collective and Stochastic Motion in the Time-Dependent Schrodinger Equation Part 3: Propagators

2021
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Zenodo
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In a previous note (1) Part 2, we compared two approaches to solving the Schrodinger equation: id/dt (partial) W(x,t) = -1/2m d/dx d/dx W + .5kxx W + f(t)x W ((1)), with both utilizing the idea of a transformation, namely y=x-b(t). The first approach involved unitary transformations, while the second changing variables and searching for a product wavefunction WoW1 such that Wo satisfies the oscillator equation without f(t)x (but with a c(t)W term easily handled by a time phase) and W1 satisfies

doi:10.5281/zenodo.4521305
fatcat:brsatl5nnrcibkqj6arm3cjg4y