Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states

Abstract

Using the transformations from paper I, we show that the Schrödinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is deomonstrated.

LaTeX, 22 pages, new format, edited, with added discussion of the classical motion

References in corpus (4)

• Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System
• Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras
• Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations
• Displacement-Operator Squeezed States. II. Examples of Time-Dependent Systems Having Isomorphic Symmetry Algebras

Cited by in corpus (4)

• Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations
• Global Symmetries of Time-Dependent Schrodinger Equations
• 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