# Response to: [Comment on Quantization of the damped harmonic oscillator [Serhan et al, J. Math. Phys. 59, 082105 (2018)]]

## TL;DR

This paper defends the quantization approach of the damped harmonic oscillator by emphasizing the importance of Hermiticity and correct application of the Nikiforov-Uvarov method, correcting previous calculation errors.

## Contribution

It clarifies the correct procedure for quantizing the damped harmonic oscillator, highlighting the need for Hermiticity and proper method application to obtain real energy eigenvalues.

## Key findings

- Incorrect calculation in previous comment affected eigenvalues
- Hermiticity achieved via symmetrization yields real eigenvalues
- Correct application of Nikiforov-Uvarov method confirms original results

## Abstract

This is a response to a recently reported comment [1] on paper [J. Math. Phys.59, 082105 (2018)] regarding the quantization of damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of [2] 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 firstly achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. Applying the canonical quantization on the resulted Hermitian Hamiltonian and then using the Nikiforov-Uvarov method correctly, the energy eigenvalues will be real and exactly as given by Eq. (35) of [2].