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On Aharonov–Casher bound states

  • E. O. Silva
  • F. M. AndradeEmail author
  • C. Filgueiras
  • H. Belich
Regular Article - Theoretical Physics

Abstract

In this work bound states for the Aharonov–Casher problem are considered. According to Hagen’s work on the exact equivalence between spin-1/2 Aharonov–Bohm and Aharonov–Casher effects, is known that the E term cannot be neglected in the Hamiltonian if the spin of particle is considered. This term leads to the existence of a singular potential at the origin. By modeling the problem by boundary conditions at the origin which arises by the self-adjoint extension of the Hamiltonian, we derive for the first time an expression for the bound state energy of the Aharonov–Casher problem. As an application, we consider the Aharonov–Casher plus a two-dimensional harmonic oscillator. We derive the expression for the harmonic oscillator energies and compare it with the expression obtained in the case without singularity. At the end, an approach for determination of the self-adjoint extension parameter is given. In our approach, the parameter is obtained essentially in terms of physics of the problem.

Keywords

Wave Function Arbitrary Parameter Polar Coordinate System Bound State Energy Irregular Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors would like to thank F. Moraes for their critical reading of the manuscript, and for helpful discussions. E.O. Silva acknowledges research grants by CNPq-(Universal) project No. 484959/2011-5, H. Belich and C. Filgueiras acknowledges research grants by CNPq (Brazilian agencies).

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • E. O. Silva
    • 1
  • F. M. Andrade
    • 2
    Email author
  • C. Filgueiras
    • 3
  • H. Belich
    • 4
  1. 1.Departamento de FísicaUniversidade Federal do MaranhãoSão LuísBrazil
  2. 2.Departamento de Matemática e EstatísticaUniversidade Estadual de Ponta GrossaPonta GrossaBrazil
  3. 3.Departamento de FísicaUniversidade Federal de Campina GrandeCampina GrandeBrazil
  4. 4.Departamento de Física e QuímicaUniversidade Federal do Espírito SantoVitóriaBrazil

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