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- Title
Lie algebraic treatment of the quadratic invariants for a quantum system.
- Authors
Abdalla, M. Sebawe; Leach, P. G. L.
- Abstract
We consider the problem of the time-dependent degenerate parametric amplifier. We obtain the quadratic invariant and use it to derive the wave function via its su (1, 1) algebraic basis and a unitary transformation to the time-dependent Schrödinger equation for the parametric amplifier. We obtain the real and the complex invariants, which we use to solve the time-dependent Cauchy problem. Using different integrability conditions, we find the most general solution, which we analyze extensively, providing details of the calculations.
- Subjects
ALGEBRAIC functions; LIE algebras; QUADRATIC equations; WAVE functions; CAUCHY problem
- Publication
Theoretical & Mathematical Physics, 2009, Vol 159, Issue 1, p535
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1007/s11232-009-0043-1