Estado coerente para o oscilador de Dirac via Álgebra de Wigner-Heisenberg.

Abstract

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.