ALVES, A. L.; http://lattes.cnpq.br/9783937217317401; ALVES, André de Lima.
Resumo:
The coherent states are observed in a very wide range of physical systems, which
enables their study and applications in various areas of science. We will present a brief
historical discussion and a small analysis of the algebraic treatment for the coherent
states of the simple harmonic oscillator. We will present the Wigner-Heisenberg algebra
(WH) and the algebraic method for the generalized oscillator developed by Jayaraman
and Rodrigues [1].In this work, we will investigate the coherent states of the
Dirac oscillator for the three-dimensional case in the context of the Wigner-Heisenberg
algebra. In doing so, a connection is established between the Dirac Hamiltonian ( ˜HD),
and the Wigner Hamiltonian (HW) in perspective of the determination of the energy
spectrum and the eigenfunctions of the Dirac oscillator. We use the supersymmetry
technique (SUSY) as an algebraic resource to evidence the relationship between
Wigner’s Hamiltonian and the supersymmetric three-dimensional isotropic harmonic
oscillator.