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European Journal of Physics

Reply to Comments on ‘Wave-like variables of a classical particle and their connections to quantum mechanics’ ( Eur. J. Phys. 2017, 38 , 015401)

Chen Yang

Published Feb 24, 2026• 0 citations
Publisher

Abstract

Abstract In the commentary (Comments on ‘Wave-like variables of a classical particle and their connections to quantum mechanics’ Eur. J. Phys. 2017, 38, 015401), the authors only consider the trivial solution (e.g. real constant) of the dynamical variables and did not see the non-trivial solution that carried the magnitude and phase. The validation of wave-like solution is provided as a simple example from complex analysis.

DOI
10.1088/1361-6404/ae126b

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Comments on ‘Wave-like variables of a classical particle and their connections to quantum mechanics’ (Eur. J. Phys. 38, 015401, 2017)

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Abstract We report about some obvious and severe flaws in Chen Yang’s paper titled ‘Wave-like variables of a classical particle and their connections to quantum mechanics,’ published in the Eur. J. Phys. 38 015401, (2017) and in a follow-up paper of the same author, where the errors are repeated, namely Eur. J. Phys. 39 035406, (2018).

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The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.

arXiv:1805.01986•May 5, 2018•0 citations
Abstract In the commentary (Comments on ‘Wave-like variables of a classical particle and their connections to quantum mechanics’ Eur. J. Phys. 2017, 38, 015401), the authors only consider the trivial solution (e.g. real constant) of the dynamical variables and did not see the non-trivial solution that carried the magnitude and phase. The validation of wave-like solution is provided as a simple example from complex analysis.
Abstract In many texts, the transition from classical mechanics to quantum mechanics is achieved by substituting the action for the phase angle. The paper presents a different approach to show some connections between classical and quantum mechanics for a single particle for an audience at graduate and postgraduate levels. Firstly, it is shown that a wave equation of action can be derived under the free particle condition and the Legendre transform. The wave-like solutions of the action, Hamiltonian and momentum of the free particle are presented. Using the discrete approximation, the equation of motion of a single particle, in scalar potential field, is obtained in a similar form to Schrödinger’s equation. The rest of the paper discusses the propagation, superposition of the wave-like dynamic variables and their connections to quantum mechanics. The superposition of the variables of a particle is generally distinct from the superposition of classical waves (e.g. acoustics). The quantum superposition provides a self-consistent interpretation of the wave-like solutions of the variables. Connections between the classical and quantum relations for corresponding variables are observed from the one-to-one comparisons.
We contend that the statement attributing to us the implication that the wave functions ?I(x, t) and ?II(x, t) are different cannot not be logically supported. On the contrary, throughout our paper ?Overcoming misconceptions in quantum mechanics with the time evolution operator? (Garcia Quijas and Ar?valo Aguilar 2007 Eur. J. Phys. 28 147) we constructed an argument to give support to the statement that the two wave functions ?I(x, t) and ?II(x, t) are the same. In other words, in our paper we really did appreciate that methods I and II lead to identical results.
The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.