Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations

Abstract

In this paper, we focus on a general class of Schrödinger equations that are time-dependent and quadratic in X and P. We transform Schrödinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ``time'' variable. We derive mathematical constraints forthe transformation and introduce two examples.

LaTeX, 18 pages, new format, edited

References in corpus (3)

• Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras
• Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states
• Displacement-Operator Squeezed States. II. Examples of Time-Dependent Systems Having Isomorphic Symmetry Algebras

Cited by in corpus (3)

• Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states
• The Schrödinger system H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b 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