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

Michael Martin Nieto·D. Rodney Truax
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Abstract

We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to a different time-dependent quadratic Schrödinger equations (TQ) and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-time symmetries, the number states, the squeezed-state and (with their classical motion), (Δx)^2, (Δp)^2, and the uncertainty product.

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Michael Martin Nieto, D. Rodney Truax. 2002-01-21. The Schrödinger system H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2. https://doi.org/10.1006/aphy.2001.6145

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