Skip to main content

Aharonov-Bohm Effect: The Principle Behind the Interaction of Electrons with Electromagnetic Fields

  • Chapter
  • 137 Accesses

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 70))

Abstract

In 1959, Aharonov and Bohm presented a paper entitled “Significance of electromagnetic potentials in quantum theory” [6.1]. Its content can be roughly summarized as follows: In classical electrodynamics, potentials are merely a convenient mathematical tool for calculations concerning electromagnetic fields. The fundamental equations can always be formulated using these fields. However, in quantum mechanics potentials cannot be eliminated from the Schrödinger equation and consequently seem to have physical significance. Aharonov and Bohm went beyond this conjecture and proposed actual electron-interference experiments. These experiments were intended to clarify how potentials affect electrons passing through field-free regions. The phenomenon these researchers described came to be called the Aharonov-Bohm (AB) effect in their honor.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Aharonov, D. Bohm: Significance of electromagnetic potentials in quantum theory. Phys. Rev. 115, 485 (1959)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. M. Peshkin, A. Tonomura: The Aharonov-Bohm Effect, Lect. Notes Phys., Vol. 340 (Springer, Berlin, Heidelberg 1989)

    Book  Google Scholar 

  3. T.T. Wu, C.N. Yang: Concept of nonintegrable phase factors and global formulation of gauge fields. Phys. Rev. D 12, 3845 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  4. C.N. Yang, R.L. Mills: Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96, 191 (1956)

    Article  MathSciNet  ADS  Google Scholar 

  5. R. Utiyama: Invariant theoretical interpretation of interaction. Phys. Rev. 101, 1597 (1956)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. S. Weinberg: A model of leptons. Phys. Rev. Lett. 19, 1264 (1967)

    Article  ADS  Google Scholar 

  7. A. Salam: Weak and electromagnetic interactions. Proc. 8th Int’l Symp. on Elementary Particle Theory, ed. by N. Svartholm (Almqvist & Wilksells, Stockholm 1968) pp.367–377

    Google Scholar 

  8. H.J. Bernstein, A.V. Philips: Fiber bundles and quantum theory. Sci. Am. 245, 95 (1981)

    Article  Google Scholar 

  9. R.G. Chambers: Shift of an electron interference pattern by enclosed magnetic flux. Phys. Rev. Lett. 5, 3 (1960)

    Article  ADS  Google Scholar 

  10. H.A. Fowler, L. Marton, J.A. Simpson, J.A. Suddeth: Electron interferometer studies of iron whiskers. J. Appl. Phys. 32, 1153 (1961)

    Article  ADS  Google Scholar 

  11. H. Boersch, H. Harnisch, K. Grohmann: Experimenteller Nachweis der Phasenverschiebung von Elektronenwellen durch das magnetische Vektorpotential. Z. Phys. 169, 263 (1962)

    Article  ADS  Google Scholar 

  12. G. Möllenstedt, W. Bayh: Kontinuierliche Phasenschiebung von Elektronenwellen im kraftfeldfreien Raum durch das magnetische Vektorpotential eines Solenoids. Phys. Bl. 18, 299 (1962)

    Article  Google Scholar 

  13. P. Bocchieri, A. Loinger: Nonexistence of the Aharonov-Bohm effect. Nuovo Cimento A 47, 475 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  14. P. Bocchieri, A. Loinger, G. Siragusa: Nonexistence of the Aharonov-Bohm effect. II Discussion of the Experiments. Nuovo Cimento A 51, 1 (1979)

    Article  ADS  Google Scholar 

  15. D. Home, S. Sengupta: A critical reexamination of the Aharonov-Bohm effect. Am. J. Phys. 51, 942 (1983)

    Article  ADS  Google Scholar 

  16. S.M. Roy: Condition for nonexistence of Aharonov-Bohm effect. Phys. Rev. Lett. 44, 111 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  17. W. Ehrenberg, R.W. Siday: The refractive index in electron optics and the principles of dynamics. Proc. Phys. Soc. London B 62, 8 (1949)

    Article  ADS  MATH  Google Scholar 

  18. D. Bohm, B.J. Hiley: On the Aharonov-Bohm effect. Nuovo Cimento A 52, 295 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  19. T. Takabayasi: Hydrodynamical formalism of quantum mechanics and Aharonov-Bohm effect. Prog. Theor. Phys. 69, 1323 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. P. Bocchieri, A. Loinger, G. Siragusa: The role of the electromagnetic potentials in quantum mechanics. The Marton experiment. Nuovo Cimento A 56, 55 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  21. C.G. Kuper: Electromagnetic potential in quantum mechanics: a proposed test of the Aharonov-Bohm effect. Phys. Lett. A 79, 413 (1980)

    Article  ADS  Google Scholar 

  22. V.L. Lyuboshitz, Ya.A. Smorodinskii: The Aharonov-Bohm effect in a toroidal solenoid. Sov. Phys. JETP 48, 19 (1978)

    ADS  Google Scholar 

  23. A. Tonomura, T. Matsuda, R. Suzuki, A. Fukuhara, N. Osakabe, H. Umezaki, J. Endo, K. Shinagawa, Y. Sugita, H. Fujiwara: Observation of the Aharonov-Bohm effect by electron holography. Phys. Rev. Lett. 48, 1443 (1982)

    Article  ADS  Google Scholar 

  24. A. Tonomura, T. Matsuda, J. Endo, T. Arii, K. Mihama: Direct observation of fine structure of magnetic domain walls by electron holography. Phys. Rev. Lett. 44, 1430 (1980)

    Article  ADS  Google Scholar 

  25. A. Fukuhara, K. Shinagawa, A. Tonomura, H. Fujiwara: Electron holography and magnetic specimens. Phys. Rev. B 27, 1839 (1983)

    Article  ADS  Google Scholar 

  26. P. Bocchieri, A. Loinger, G. Siragusa: Remarks on “Observation of Aharonov-Bohm effect by electron holography”. Lett. Nuovo Cimento 35, 370 (1982)

    Article  Google Scholar 

  27. H. Miyazawa: Quantum mechanics in a multiply-connected region. Proc. 10th Hawaii Conf. High Energy Physics, Hawaii (University of Hawaii 1985) pp.441–458

    Google Scholar 

  28. E. Schrödinger: Die Mehrdeutigkeit der Wellenfunktion. Ann. Phys. 32, 49 (1938)

    Article  MATH  Google Scholar 

  29. W. Pauli: Über ein Kriterium für Ein- oder Zweiwertigkeit der Eigenfunktionen in der Wellenmechanik. Helv. Phys. Acta 12, 147 (1939)

    Google Scholar 

  30. A. Tonomura, N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, S. Yano, H. Yamada: Evidence for the Aharonov-Bohm effect with magnetic field completely shielded from electron wave. Phys. Rev. Lett. 56, 792 (1986)

    Article  ADS  Google Scholar 

  31. A. Tonomura, S. Yano, N. Osakabe, T. Matsuda, H. Yamada, T. Kawasaki, J. Endo: Proof of the Aharonov-Bohm effect with completely shielded magnetic field. Proc. 2nd Int’l Symp. Foundations of Quantum Mechanics, Tokyo 1986, ed. by M. Namiki, Y. Ohnuki, Y. Murayama, S. Nomura (Phys. Soc. Jpn., Tokyo 1987) pp.97–105

    Google Scholar 

  32. N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, A. Tonomura, S. Yano, H. Yamada: Experimental confirmation of the Aharonov-Bohm effect using a toroidal magnetic field confined by a superconductor. Phys. Rev. A 34, 815 (1986)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tonomura, A. (1993). Aharonov-Bohm Effect: The Principle Behind the Interaction of Electrons with Electromagnetic Fields. In: Electron Holography. Springer Series in Optical Sciences, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13913-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-13913-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-13915-8

  • Online ISBN: 978-3-662-13913-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics