2015/03/31 by A. M. Gavrilik, I. I. Kachurik · 1 citation
Physics and Astronomy · #quant-ph #hep-th
paper · pdf · doi:10.1142/s0217732316500243
published as Mod. Phys. Lett. A, Vol. 31, No. 4 (2016) 1650024 · v2: 15 pages, clarifying text added in sec.3, title slightly changed, matches published version
arxiv created 2016/01/21 · arxiv updated 2016/01/22
The recently introduced two- and three-parameter (p,q)- and (p,q,μ)-deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective nonstandard (other than known ones) deformed quantum oscillator algebras. In this paper we show that such connection dictates certain new η(N)-pseudo-Hermitian conjugation rule between the creation and annihilation operators, with η(N) depending on the particle number operator N. In turn, that leads to the related η(N)-pseudo-Hermiticity of the position/momentum operators, though the involved Hamiltonian is Hermitian. Different possible cases are studied, and some interesting features implied by the use of such η(N)-based conjugation rule are emphasized.