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Journal of Mathematical Physics

Comment on “Coherent states for the nonlinear harmonic oscillator” [J. Math. Phys. 53, 062104 (2012)]

Naila Amir, Shahid Iqbal

Published Nov 1, 2014• 11 citations
Publisher

Abstract

We argue that the first order corrected computational scheme, used by Ghosh [J. Math. Phys. 53, 062104 (2012)] to obtain eigenenergies, corresponding generalized coherent states and various expectation values, is illegitimate. Consequently, the results presented in the work of Ghosh are incorrect and the corresponding conclusions are misleading.

DOI
10.1063/1.4901559

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We argue that the first order corrected computational scheme, used by Ghosh [J. Math. Phys. 53, 062104 (2012)] to obtain eigenenergies, corresponding generalized coherent states and various expectation values, is illegitimate. Consequently, the results presented in the work of Ghosh are incorrect and the corresponding conclusions are misleading.
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 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)].