Bohm potential for the time dependent harmonic oscillator

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2021
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Bohm potential for the time dependent harmonic oscillator
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In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.
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DOI: 10.1063/5.0044144
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Journal of Mathematical Physics Volume 62 Issue 12 Article Number 122103 Dec 1 2021
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