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We introduce an alternative factorization of the Hamiltonian of the quantumharmonic oscillator which leads to a two-parameter self-adjoint operator fromwhich the standard harmonic oscillator, the one-parameter oscillatorsintroduced by Mielnik, and the Hermite operator are obtained in certain limitsof the parameters. In addition, a single Bernoulli-type parameter factorizationwhich 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 partof this work

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