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A New Version of the Aharonov–Bohm Effect

Abstract

We propose a simple situation in which the magnetic Aharonov–Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whether the particle interacts with the solenoid or not. Even with the particle excluded from the magnetic field, the number of self-adjoint extensions of the initial Hamiltonian depends on the magnetic flux. This is a new point of view of the Aharonov–Bohm effect.

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Acknowledgements

CRdO thanks the partial support by CNPq (a Brazilian government agency, under contract 303503/2018-1).

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Correspondence to César R. de Oliveira.

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de Oliveira, C.R., Romano, R.G. A New Version of the Aharonov–Bohm Effect. Found Phys (2020). https://doi.org/10.1007/s10701-020-00328-6

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Keywords

  • Aharonov–Bohm effect
  • Self-adjoint extensions
  • Magnetic potential