Theory of representations and parametric excitation of quantum systems
Abstract
The paper reviews results pertaining to the parametric excitation of quantum systems with dynamic symmetry. Particular attention is given to a nonstationary onedimensional singular quantum oscillator, the example of a system with a dynamic symmetry group. Explicit expressions are obtained for the evolution operator, density matrix, and correlation functions of this system. In addition, sumrule and generatingfunction formulas are obtained for Jacobi, Legendre, and Laguerre polynomials. Finally, the parametric excitation of more complex systems corresponding to Lie algebras of higher dimensionality are examined, and some applications of the results obtained are considered.
 Publication:

IN: Group theory
 Pub Date:
 1986
 Bibcode:
 1986gtge.book..162D
 Keywords:

 Group Theory;
 Nonstabilized Oscillation;
 Quantum Mechanics;
 Symmetry;
 Correlation;
 Hamiltonian Functions;
 Lie Groups;
 Parametric Amplifiers;
 Sum Rules;
 Physics (General)