On Aharonov-Casher bound states

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 $\nabla \cdot \mathbf{E}$ 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.

11 pages, matches published version

References in corpus (19)

• Aharonov-Bohm-Casher Problem with a nonminimal Lorentz-violating coupling
• Topology, Locality, and Aharonov-Bohm Effect with Neutrons
• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
• Relativistic Landau-Aharonov-Casher quantization based on the Lorentz symmetry violation background
• Relativistic Landau quantization for a neutral particle
• Long Range Effects of Cosmic String Structure
• The Noncommutative Anandan's Quantum Phase
• Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• On the quantum dynamics of a point particle in conical space
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background
• Quantum mechanics of a free particle on a pointed plane revisited
• Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem
• Mathematical justification of the Aharonov-Bohm hamiltonian
• A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential
• Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
• Dipole binding in a cosmic string background due to quantum anomalies
• Comment on "Relativistic Aharonov-Bohm effect in the presence of planar Coulomb potentials"

Cited by in corpus (17)

• Bound states of massive fermions in the Aharonov--Bohm-like fields
• On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation
• Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms
• Creation of planar charged fermions in Coulomb and Aharonov-Bohm potentials
• On the Aharonov-Casher scattering in a CPT-odd Lorentz-violating background
• The influence of Aharonov-Casher effect on the generalized Dirac oscillator in the cosmic string space-time
• Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin
• On planar quantum dynamics of a magnetic dipole moment in the presence of electric and magnetic fields
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings
• Effect of vacuum polarization of charged massive fermions in an Aharonov--Bohm field
• Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime
• Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Algebraic solution and coherent states for the Dirac oscillator interacting with the Aharonov-Casher system in the cosmic string background
• Optical and spin-optical superpositions modulated by Aharonov-Bohm effect
• Quantum states of a neutral massive fermion with an anomalous magnetic moment in an external electric field
• Quantum Hall-like effect for neutral particles with magnetic dipole moments in a quantum dot