The Heisenberg oscillator

Dirac Oscillator via R-deformed Heisenberg Algebra

The complete energy spectrum for the Dirac oscillator via R-deformed Heisenberg algebra is investigated. PACS numbers: 11.30.Pb, 03.65.Fd, 11.10.Ef. To appear in the proceedings at the XXIII Brazilian National Meeting on Particles and Fields, October 15 to 19, 2002, Águas de Lindóia-SP, Brazil, site www.sbf1.if.usp.br/eventos/enfpc/xxiii.

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator.

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases. ∗Electronic address: [email protected] †Electr...

A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras

A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains null vectors and so is reducible to a finite dimensional representation. The cyclic, nilpotent and unitary representations are discussed. Witten’s deformation ...

Some geometrical properties of the oscillator group

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

Hq(4) Symmetry: The Linear q-Harmonic Oscillator Based on Generalized Irreps of the q-Deformed Heisenberg Algebra