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Time-dependent mass Schr\"odinger equations. II. Example 1

Michael Martin Nieto, D. Rodney Truax

Published Nov 20, 1999• 0 citations
OpenAlex

Abstract

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

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