Estados coerentes para o oscilador isotônico via a super-realização da álgebra de Wigner-Heisenberg.

Abstract

In this work it is determined the Isotonic Oscillator's Coherent States. This was achieved using the Wigner-Heisenberg algebra and the application of Supersymmetry in Quantum Mechanics (SUSY). The interaction between the Wigner-Heisenberg algebra and supersymmetry algebra allowed identification the bosonic and fermionic sectors and their energy spectra. From this sectorization, were built for the Isotonic Oscillator Coherent States for the bosonic sector. Also, it were analyzed the main properties of these states, like non-orthogonality, relation of supercompleteness and the relation of minimum uncertainty, of which the first two are consistent with the properties of Coherent States of the Harmonic Oscillator. By analyzing the relation of minimum uncertainty for these states, it was found that for some parameters the intensity of centripetal barrier / eigenstates of position or momentum are obtained.