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A unified algebraic dynamical solution to general two-photon algebrasystems

Ying, ZJWang

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

We use squeezing and displacement operators and apply algebraic We use squeezing and displacement operators and apply algebraic

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Using an algebraic approach, we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder-operator and the displacement-operator methods, showing the equivalence between the two procedures. We obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce. In a second approach, we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators (in the first case) and the combined action of these operators (in the second case). We apply the generalized approach for shape-invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states.
We consider quantum confined systems represented by supersymmetric quantum mechanics where the Hamiltonians are products of two operators. We introduce inverses of these operators as well as pair operators, which are products of the original operators and their inverses. We show that the eigenstates of these pair operators are purely squeezed states, and using them we construct raised and decreased extensions of the squeezed states. We apply this procedure both to the ladder-operator and to the displacement-operator methods, showing the equivalence between those the two approaches. Finally, we show how the raised and decreased squeezed states can be dynamically produced by coupling the Hamiltonian with a two-level atom.