SL(3,R) realisations and the damped harmonic oscillator
- 21 June 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (9) , 1777-1786
- https://doi.org/10.1088/0305-4470/17/9/013
Abstract
The point and contact Lie groups for the damped harmonic oscillator are found and several realisations of the SL(3,R) Lie group are analysed. The non-critical and critical cases are studied separately and a sort of limiting procedure is defined, which leaves the Lie algebra structure unchanged. Some physical applications of these results are also pointed out.Keywords
This publication has 14 references indexed in Scilit:
- Contact symmetries of general linear second-order ordinary differential equationsJournal of Physics A: General Physics, 1983
- Bohlin’s and other integrals for the damped harmonic oscillatorAmerican Journal of Physics, 1981
- Sl(3,R) and the repulsive oscillatorJournal of Physics A: General Physics, 1980
- Symmetries of the time-dependent N-dimensional oscillatorJournal of Physics A: General Physics, 1980
- The complete symmetry group of the one-dimensional time-dependent harmonic oscillatorJournal of Mathematical Physics, 1980
- Symmetry groups and conserved quantities for the harmonic oscillatorJournal of Physics A: General Physics, 1978
- Contact transformations. IV. Contraction of contact Lie algebrasInternational Journal of Theoretical Physics, 1977
- Contact transformations and conformal group. III. Finite nonrelativistic transformationsInternational Journal of Theoretical Physics, 1977
- Contact transformations and conformal group. II. Non-relativistic theoryInternational Journal of Theoretical Physics, 1975
- Contact transformations and conformal group. I. Relativistic theoryInternational Journal of Theoretical Physics, 1975