On the bound states for the Aharonov-Casher systems

Details On the bound states for the Aharonov-Casher systems On the bound states for the Aharonov-Casher systems

2012-03-14

arxiv.org/abs/1203.3096v1

Physics

Quantum Physics

26 pages, submitted to Annals of Physics

Scientific paper

The bound states for the Aharonov-Casher problem is considered. According to the Hagen's work on the exact equivalence between spin-1/2 Aharonov-Bohm and Aharonov-Casher effects, is known that the $\boldsymbol{\nabla}\cdot\mathbf{E}$ term can not be neglected in the Hamiltonian if the spin of particle is considered. We then use the method of self-adjoint extension to study the behavior of wave functions at origin. By modeling the problem by boundary conditions, we derive the for the first time, the expression for the bound state energy of pure 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 energy 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. This parameter is obtained essentially in terms of physics of the problem.

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