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Schrödinger equations with time-dependent P^2 and X^2 terms

Michael Martin Nieto·D. Rodney Truax
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Abstract

We present some general results for the time-dependent mass Hamiltonian problem with H=-{1/2}e^{-2ν}\partial_{xx} +h^{(2)}(t)e^{2ν}x^2. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P^2 and X^2 terms. We give the specific transformations to a different quantum Schrödinger(TQ) equation and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-time symmetries and (x,t) representations for number states, coherent states, and squeezed states. These general results include earlier work as special cases.

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Michael Martin Nieto, D. Rodney Truax. 2002-01-21. Schrödinger equations with time-dependent P^2 and X^2 terms. https://arxiv.org/abs/quant-ph/9911093

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