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arXiv · 1209.4429

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

R. Arcos-Olalla·M. A. Reyes·H. C. Rosu
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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

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R. Arcos-Olalla, M. A. Reyes, H. C. Rosu. 2012-09-20. An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators. https://doi.org/10.1016/j.physleta.2012.09.024

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