An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators
Mathematical Physics
2013-12-24 v1 math.MP
Abstract
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization which is different of the one introduced by M. A. Reyes, H. C. Rosu, and M. R. Gutierrez, Phys. Lett. A 375 (2011) 2145 is briefly discussed in the final part of this work
Keywords
Cite
@article{arxiv.1209.4429,
title = {An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators},
author = {R. Arcos-Olalla and M. A. Reyes and H. C. Rosu},
journal= {arXiv preprint arXiv:1209.4429},
year = {2013}
}
Comments
18 pages, 7 figures, last 2 figures are not included in the version to be published, accepted by Phys. Lett. A