Response to "Comment on `Quantization of the damped harmonic oscillator'" [J. Math. Phys. 60, 094101 (2019)]
Abstract
This is a response to a recently reported comment [F. M. Fernández, J. Math. Phys. 60, 094101 (2019)] on paper [M. Serhan et al., J. Math. Phys. 59, 082105 (2018)] regarding the quantization of the damped harmonic oscillator using a nonHermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)] is incorrect, and thus the subsequent steps via the NikiforovUvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be first achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. The canonical quantization on the resulted Hermitian Hamiltonian yields the real energy eigenvalues as exactly given by Eq. (35) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)].
 Publication:

Journal of Mathematical Physics
 Pub Date:
 September 2019
 DOI:
 10.1063/1.5125816
 arXiv:
 arXiv:1903.00352
 Bibcode:
 2019JMP....60i4102S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 2 pages, no figure no table