The quantum deformation of SU(1, 1) as the dynamical symmetry of the anharmonic oscillator
- 21 April 1991
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 24 (8) , 1699-1707
- https://doi.org/10.1088/0305-4470/24/8/013
Abstract
As an application of q-deformed algebras to standard quantum mechanics, the author shows that the SU(1, 1) dynamical symmetry of the quantum harmonic oscillator is deformed, in the first order of approximation, to the dynamical symmetry defined by the quantized universal enveloping algebra of SU(1, 1) when the harmonic potential is perturbed with a potential in x4. The resolution of the anharmonic oscillator is carried out algebraically in terms of generalized lowering and rising operators.Keywords
This publication has 13 references indexed in Scilit:
- Deforming maps for quantum algebrasPhysics Letters B, 1990
- Gauge theories, vertex models, and quantum groupsNuclear Physics B, 1990
- “SUPERRADIANCE” EFFECT IN A GRAVITATIONAL ANTENNAModern Physics Letters A, 1990
- Common structures between finite systems and conformal field theories through quantum groupsNuclear Physics B, 1990
- Duality and quantum groupsNuclear Physics B, 1990
- On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)qJournal of Physics A: General Physics, 1989
- The quantum group SUq(2) and a q-analogue of the boson operatorsJournal of Physics A: General Physics, 1989
- Twisted $\textit{SU}(2)$ Group. An Example of a Non-Commutative Differential CalculusPublications of the Research Institute for Mathematical Sciences, 1987
- A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equationLetters in Mathematical Physics, 1986
- Aq-difference analogue of U(g) and the Yang-Baxter equationLetters in Mathematical Physics, 1985