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

R. Y. Chiao*, H. Hart†, M. Scheibner‡, and J. Sharping§

N. A. Inan∥

D. A. Singleton

M. E. Tobar**

  • *Contact author: raymond_chiao@yahoo.com
  • †Contact author: hhart3@ucmerced.edu
  • ‡Contact author: mscheibner@ucmerced.edu
  • §Contact author: jsharping@ucmerced.edu
  • ∥Contact author: ninan@ucmerced.edu
  • Contact author: dougs@mail.fresnostate.edu
  • **Contact author: michael.tobar@uwa.edu.au
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Phys. Rev. A 111, 066204 – Published 13 June, 2025

DOI: https://doi.org/10.1103/mtfh-m6tr

Abstract

We respond to the points raised in the preceding Comment [Phys. Rev. A 111, 066203 (2025)] on our recent work [Phys. Rev. A 107, 042209 (2023)], 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.

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Comments & Replies

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

Shan Gao
Phys. Rev. A 111, 066203 (2025)

Article Text

Original Article

Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect

R. Y. Chiao, H. Hart, M. Scheibner, J. Sharping, N. A. Inan, D. A. Singleton, and M. E. Tobar
Phys. Rev. A 107, 042209 (2023)

References (6)

  1. S. Gao, preceding Comment, Phys. Rev. A 111, 066203 (2025).
  2. R. Y. Chiao, H. Hart, M. Scheibner, J. Sharping, N. A. Inan, D. A. Singleton, and M. E. Tobar, Phys. Rev. A 107, 042209 (2023).
  3. R. Y. Chiao, N. A. Inan, M. Scheibner, J. Sharping, D. A. Singleton, and M. E. Tobar, Phys. Rev. D 109, 064073 (2024).
  4. D. J. Griffith, Introduction to Quantum Mechanics, 2nd ed. (Pearson Prentice Hall, Upper Saddle River, 2005).
  5. D. Tong, arXiv:1606.06687.
  6. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).

Outline

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Phys. Rev. A 111, 066204– Published 13 June, 2025
  • Received 27 April 2025
  • Accepted 29 May 2025
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