Interpreting Bohm-like quantum potentials in "Computing quantum waves exactly from classical action"

Abstract

In contrast to his earlier posting arXiv260502621 [6] commenting on the article rspa20250413 [5] and answered in arXiv260520443 [3] the same author of the new posting arXiv260605197 [7] does not seem to dispute any longer the following points i Assuming in [5] that along each extremal action path the action Laplacian or more generally the propagated density is space independent implies that the Bohm like potential terms are exactly zero a condition which is directly verified in all examples of [5] as well as in its relativistic Dirac and Maxwell extensions ii Just as in Feynmans well known results the standard polynomials in the treatment in [5] of the harmonic oscillator appear naturally from the Taylor expansion of the kernel and thus there is no circularity. He does not appear to dispute either that Bohm like terms along individual stationary action paths are indeed very different from the standard Bohm Madelung potential on the overall wave. This is illustrated e.g. in the detailed double slit example in [3] whose Bohm like terms are exactly zero while the usual Bohm Madelung potential can be very large. Also in that example the action behind the slits is a conic function so that exact Feynman or Van Vleck computations based on quadratic actions do not apply. His new posting [7] therefore concentrates on the claim in [3] that the space independence assumption on the Laplacian of the action if not directly verified can be achieved through time rescaling which is a fair discussion topic We all agree that the Schrodinger equation has to be fulfilled in the original x t coordinates. To this effect as in the hydrogen atom example of the original paper [5] we use a general result of Duru and Kleinert which the author of [6] and [7] may be unaware of. There independence of the constructed eigenwave on the rescaled time is key to the exact backmapping to the original x t coordinates.