The Schrödinger System H=-12(tot)a∂xx+12ω2(tto)bX2

Author： Nieto M.M.   Truax D.R.  

Publisher： Elsevier

ISSN： 0003-4916

Source： Annals of Physics, Vol.292, Iss.1, 2001-08, pp. : 23-41

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Abstract

We attack the specific time-dependent Hamiltonian problem H=-12(tot)a∂xx+12ω2(tto)bx2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to a different time-dependent quadratic Schrödinger equation (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 〈x〉 and 〈p〉 (with their classical motion), (Δx)2, (Δp)2, and the uncertainty product.

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