© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Comment on ‘‘Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfest’s theorem’’

Mark D. Semon, John R. Taylor

Published Aug 1, 1994• 4 citations

Abstract

In a recent paper [D. H. Kobe, V. C. Aguilera-Navarro, and R. M. Ricotta, Phys. Rev. A 45, 6192 (1992)], Kobe et al. have calculated the expectation values of position and momentum in the Aharonov-Bohm effect and have found that both are shifted by the Aharonov-Bohm potentials. Although these shifts appear to contradict certain ``no-shift'' theorems proved by various authors, we show that this apparent contradiction is the result of different assumptions. Specifically, one of the assumptions on which the no-shift theorems are based does not hold for the parameters used by Kobe et al.; that is, with their parameters, there is no reason to expect the no-shift theorems to hold. On the other hand, with the parameters of actual two-slit experiments, all of the conditions of the no-shift theorems do hold and the no-shift theorems do apply.

DOI: 10.1103/physreva.50.1954

Related papers

Reply to ‘‘Comment on ‘Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfest’s theorem’ ’’

Donald H. Kobe, Valdir C. Aguilera-Navarro

The assumptions under which the ``no-shift'' theorem of Semon and Taylor [preceding Comment, Phys. Rev. A 50, 1954 (1994)] is valid are examined. For some choices of possible experimental parameters, the assumptions are not satisfied.

Physical Review A•Aug 1, 1994•3 citations

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfest’s theorem

Donald H. Kobe, Valdir C. Aguilera-Navarro, Regina Maria Ricotta

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfest's theorems and the conservation of momentum are satisfied.

Physical Review A•May 1, 1992•10 citations

The Aharonov-Bohm effect in double- and single-slit diffraction

D Shapiro, Walter C. Henneberger

Single- and double-slit diffraction patterns are obtained by means of path integrals. The slit function is taken to be unity. This permits the study of the single-slit case as a limit of the double-slit case when the slit width is equal to the slit separation. Introduction of a whisker of flux at the midpoint of the space between slits gives the Aharonov-Bohm shift. In the case of a wide single slit, one obtains conditions approaching those postulated in calculations similar to the scattering calculation of Aharanov and Bohm (1959).

Journal of Physics A Mathematical and General•Sep 7, 1989•11 citations

Comment on “Biphoton double-slit experiment”

Xavier Oriols

In a recent paper [Phys. Rev. A 68, 033803 (2003)] experimental results on a double-slit configuration with two entangled bosons are presented. The authors argue that their data contradicts the de Broglie--Bohm interpretation of quantum mechanics. In this Comment we show that this conclusion is incorrect.

Physical Review A•Jan 31, 2005•10 citations

Reply to “Comment on ‘Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect' ”

R. Y. Chiao, Harold Hart, Michael Scheibner +4 more

We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

Physical Review A•May 29, 2025•0 citations

Reply to “Comment on ‘Role of potentials in the Aharonov-Bohm effect’ ”

Lev Vaidman A

The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.

arXiv:1508.00743•Physical Review A•Aug 31, 2015•34 citations

In a recent paper [D. H. Kobe, V. C. Aguilera-Navarro, and R. M. Ricotta, Phys. Rev. A 45, 6192 (1992)], Kobe et al. have calculated the expectation values of position and momentum in the Aharonov-Bohm effect and have found that both are shifted by the Aharonov-Bohm potentials. Although these shifts appear to contradict certain ``no-shift'' theorems proved by various authors, we show that this apparent contradiction is the result of different assumptions. Specifically, one of the assumptions on which the no-shift theorems are based does not hold for the parameters used by Kobe et al.; that is, with their parameters, there is no reason to expect the no-shift theorems to hold. On the other hand, with the parameters of actual two-slit experiments, all of the conditions of the no-shift theorems do hold and the no-shift theorems do apply.

Single- and double-slit diffraction patterns are obtained by means of path integrals. The slit function is taken to be unity. This permits the study of the single-slit case as a limit of the double-slit case when the slit width is equal to the slit separation. Introduction of a whisker of flux at the midpoint of the space between slits gives the Aharonov-Bohm shift. In the case of a wide single slit, one obtains conditions approaching those postulated in calculations similar to the scattering calculation of Aharanov and Bohm (1959).

We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.