An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

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 workComment: 18 pages, 7 figures, last 2 figures are not included in the version to be published, accepted by Phys. Lett.