Dynamical algebraic approach and invariants for time-dependent Hamiltonian systems in two dimensions
Authors:
- 1 December 1993
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 34 (12) , 5843-5850
Abstract
Dynamical invariants for time-dependent (TD) oscillator systems in two dimensions are derived. The applications of the dynamical algebraic approach known already for one-dimensional TD systems [R. S. Kaushal and H. J. Korsch, J. Math. Phys. 22, 1904 (1981)] are now carried out to two-dimensional TD systems. A possible generalization of Ermakov systems to higher dimensions is discussed.Keywords
This publication has 22 references indexed in Scilit:
- Quantum mechanics of a molecular system adsorbed on a dielectric surfacePhysical Review A, 1989
- Time-evolution operators for (coupled) time-dependent oscillators and Lie algebraic structure theoryPhysical Review A, 1988
- Time-dependent vector constants of motion, symmetries, and orbit equations for the dynamical system r̈=îr{[Ü(t)/U(t)]r −[μ/U(t)]r−2}Journal of Mathematical Physics, 1983
- Lie symmetries, nonlinear equations of motion and new Ermakov systemsJournal of Physics A: General Physics, 1982
- Dynamical Noether invariants for time-dependent nonlinear systemsJournal of Mathematical Physics, 1981
- Cosmological particle creationPhysical Review D, 1979
- Solution of the multidimensional quantum harmonic oscillator with time-dependent frequencies through Fourier, Hermite and Wigner transformsPhysics Letters A, 1979
- Dynamical symmetries and conserved quantitiesJournal of Physics A: General Physics, 1979
- Symmetry groups and conserved quantities for the harmonic oscillatorJournal of Physics A: General Physics, 1978
- Solution of the inverse problem of the calculus of variationsTransactions of the American Mathematical Society, 1941