Confusion about Bohm

Durgadas Datta.

W. Michael Dickson

Francisco Antônio Bezerra Coutinho, Yukihisa Nogami, J. Fernando Perez +1 more

Recently we studied self-adjoint extensions (SAEs) of the Aharonov-Bohm Hamiltonian for a charged Schrodinger particle of spin 0. In this paper we discuss the relation between the SAEs for a spinless particle and those for a spin- 1/2 particle in the same environment. We also consider SAEs when a Coulomb potential is added. We furthermore clarify a few confusing issues which have been discussed in some recent papers regarding the relativistic Dirac particle in the Aharonov-Bohm field.

Mariangiola Dezani-ciancaglini A, Stefano Guerrini, Adolfo Piperno

Winfried Lohmiller, Jean-Jacques Slotine

Comment on arXiv:2605.02621 [23] and arXiv:2606.05197 [24]: In contrast to his earlier comment [23] on rspa.2025.0413 [12] and answered in arXiv:2605.20443 [11], the same author of [24] does not seem to dispute any longer that the use in [12] of tools from Feynman's [5] namely - the kernel approach, which computes a wave starting at a given initial position or momentum, and is a key element in [12] to ensure that the Bohm-like quantum potential vanishes. This is directly verified in all examples of [12] as well as in the Pauli, Dirac and Maxwell derivations from classical action. This approach is very different from the standard Bohm-Madelung potential on the overall wave, as illustrated in detail in [11] for the two-slit experiment. - for the harmonic oscillator, the kernel computation directly from a Taylor series expansion, which does not involve any circularity. His second post [24] now - criticizes the use in [12], [11] of Duru and Kleinert's time-independent eigenwave equivalence of the original and the time-scaled Schrödinger equations [4], confusing this standard result with a multivariable chain rule in the time-dependent kernel computation from action in [12]. - claims that "The mathematical framework presented by the authors remains identical to the well-established semiclassical Van Vleck propagator [sic]" which requires that the "Hamiltonian is at most quadratic in position and momentum [sic]". This confuses a quadratic action in the vector case with a harmonic propagated density based on the Laplacian of the action (with harmonicity always fulfilled e.g., for holomorphic complex functions [10]. In addition, it ignores the extension of a real position to a complex or quaternion position or spin, the key result on multi-valued action branches (which enables a classical derivation of quantum randomness) and the quantization of classical action in [12].

F. Darabi

In some textbooks on quantum mechanics, the description of flux quantization in a superconductor ring based on the Aharonov-Bohm effect may lead some readers to a (wrong) conclusion that flux quantization occurs as well for a long solenoid with the same quantization condition in which the charge of cooper pair $2e$ is replaced by the charge of one electron $e$. It is shown how this confusion arises and how can one avoid it.