• DOI:10.1063/1.5125816
• Corpus ID: 201646324

Response to “Comment on ‘Quantization of the damped harmonic oscillator’” [J. Math. Phys. 60, 094101 (2019)]

@article{Serhan2019ResponseT,
  title={Response to “Comment on ‘Quantization of the damped harmonic oscillator’” [J. Math. Phys. 60, 094101 (2019)]},
  author={Mohammed Serhan and M. Abusini and Ahmed Al-Jamel and Husam El-Nasser and Eqab M. Rabei},
  journal={Journal of Mathematical Physics},
  year={2019}
}

• M. Serhan, M. Abusini, +2 authors Eqab M. Rabei
• Published 1 March 2019
• Physics
• Journal of Mathematical Physics

This is a response to a recently reported comment [F. M. Fernandez, 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 non-Hermitian 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 Nikiforov-Uvarov 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)].