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 one-dimensional 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, sum-rule and generating-function 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)