Reply to "Interpreting Bohm quantum potentials in `Computing quantum waves exactly from classical action'"

• URL: http://arxiv.org/abs/2606.05197v1
• Date: Fri, 22 May 2026 05:08:15 GMT
• Title: Reply to "Interpreting Bohm quantum potentials in `Computing quantum waves exactly from classical action'"
• Abstract summary: Lohmiller and Slotine argue that the spatial derivatives of the probability density amplitude vanish for the Feynman kernel.<n>A rigorous mathematical examination of this transformation reveals a violation of the multivariable chain rule.<n>The mathematical framework presented by the authors remains identical to the well-established semiclassical Van Vleck propagator.
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• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The recent arXiv posting arXiv:2605.20443 by Lohmiller and Slotine attempts to address the omission of the Bohm quantum potential in their proposed exact equivalence between classical action and the Schrödinger equation. They introduce a position-dependent time transformation to argue that the spatial derivatives of the probability density amplitude vanish for the Feynman kernel. A rigorous mathematical examination of this transformation reveals a violation of the multivariable chain rule. The spatial derivatives do not vanish in the physical reference frame. The mathematical framework presented by the authors remains identical to the well-established semiclassical Van Vleck propagator, which is exact exclusively for quadratic potentials.

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