Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras

Abstract

In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schrödinger equation for systems with potentials $V(x,\tau )=g^{(2)}(\tau )x^2+g^{(1)}(\tau )x+g^{(0)}(\tau )$. We describe a set of number-operator eigenstates states, $\{{\Psi }_n(x,\tau )\}$, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, ${\Psi }_0$, and a displacement squeeze operator derived using the Lie symmetries, we construct squeezed states and compute expectation values for position and momentum as a function of time, $\tau$. We prove a general expression for the uncertainty relation for position and momentum in terms of the squeezing parameters. Specific examples, all corresponding to choices of $V(x,\tau )$ and having isomorphic Lie algebras, will be dealt with in the following paper (II).

23 pages, LaTeX

References in corpus (1)

• Rydberg Wave Packets are Squeezed States

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