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

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

1999-11-20

arxiv.org/abs/quant-ph/9911094v2

Ann. Phys. 292 (2001) 1

Physics

Quantum Physics

Latex, 24 pages, including 3 figures and 8 tables. New title and format for journal. Conclusion added

Scientific paper

10.1006/aphy.2001.6144

In this paper, we attack the specific time-dependent Hamiltonian problem H=-{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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