A Lie algebraic approach to quadratic parametric processes in quantum optics and quantum acoustics is presented. In this approach the Heisenberg-Weyl and symplectic dynamical algebras are used to obtain a general exact solution for the time evolution operator. The solution is then applied to describe quantum mechanically the parametric process of backward-wave echo generation in dielectrics.
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S. V. Prants (1986) studied this question.
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