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The Schrödinger system H=-{1/2}e^{Υ(t-t_o)}\partial_{xx} +\lfrac{1}{2}ω^2e^{-Υ(t-t_o)}x^2

Michael Martin Nieto·D. Rodney Truax
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Abstract

In this paper, we attack the specific time-dependent Hamiltonian problem H=-{1/2}e^{Υ(t-t_o)}\partial_{xx} +\lfrac{1}{2}ω^2e^{-Υ(t-t_o)}x^2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to i) the more general quadratic (TQ) Schrödinger equation and to ii) a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-time symmetries, the number states, the coherent states, the squeezed-states and the time-dependent , , (Δx)^2, (Δp)^2, and uncertainty product.

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Michael Martin Nieto, D. Rodney Truax. 2000-02-22. The Schrödinger system H=-{1/2}e^{Υ(t-t_o)}\partial_{xx} +\lfrac{1}{2}ω^2e^{-Υ(t-t_o)}x^2. https://doi.org/10.1006/aphy.2001.6144

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