Comment on `On computing quantum waves exactly from classical action'
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909012524531712 |
|---|---|
| author | Vattay, Gabor |
| author_facet | Vattay, Gabor |
| contents | A recent article by Lohmiller \& Slotine (Proc.\ R.\ Soc.\ A \textbf{482}: 20250413) claims that the Schrödinger equation can be solved exactly using only classical least action and classical fluid density, asserting that this formulation avoids semiclassical approximations. We show that their mathematical derivation contains a foundational error. By neglecting the spatial derivatives of the probability density amplitude, the authors inadvertently omit the quantum potential -- the term originally identified by Madelung and later emphasised by Bohm. Consequently, their proposed equivalence is not exact but rather constitutes the standard semiclassical approximation. We further demonstrate that each of the paper's illustrative examples either belongs to a class where the quantum potential vanishes identically due to the geometry of the problem, or recovers the correct quantum result by importing quantum eigenfunctions through the initial conditions, thereby concealing the error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comment on `On computing quantum waves exactly from classical action' Vattay, Gabor Quantum Physics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics History and Philosophy of Physics A recent article by Lohmiller \& Slotine (Proc.\ R.\ Soc.\ A \textbf{482}: 20250413) claims that the Schrödinger equation can be solved exactly using only classical least action and classical fluid density, asserting that this formulation avoids semiclassical approximations. We show that their mathematical derivation contains a foundational error. By neglecting the spatial derivatives of the probability density amplitude, the authors inadvertently omit the quantum potential -- the term originally identified by Madelung and later emphasised by Bohm. Consequently, their proposed equivalence is not exact but rather constitutes the standard semiclassical approximation. We further demonstrate that each of the paper's illustrative examples either belongs to a class where the quantum potential vanishes identically due to the geometry of the problem, or recovers the correct quantum result by importing quantum eigenfunctions through the initial conditions, thereby concealing the error. |
| title | Comment on `On computing quantum waves exactly from classical action' |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2605.02621 |