First-Order Polynomial Heisenberg Algebras and Coherent States

Quantum Fest 2015

Castillo-Celeita, M.^1 ; Fernández, C.D.J.^1

Departamento de Física, Cinvestav, A.P. 14-740, México D.F.

07000, Mexico^1

关键词: Coherent state;    First order;    Harmonic oscillators;    Heisenberg;    Heisenberg algebras;    Weyl algebra;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/698/1/012007/pdf
DOI  :  10.1088/1742-6596/698/1/012007

来源: IOP

【 摘 要 】

The polynomial Heisenberg algebras (PHA) are deformations of the Heisenberg- Weyl algebra characterizing the underlying symmetry of the supersymmetric partners of the Harmonic oscillator. When looking for the simplest system ruled by PHA, however, we end up with the harmonic oscillator. In this paper we are going to realize the first-order PHA through the harmonic oscillator. The associated coherent states will be also constructed, which turn out to be the well known even and odd coherent states.