Aharonov-Bohm Effect with $\delta$--type Interaction

Abstract

A quantum particle interacting with a thin solenoid and a magnetic flux is described by a five-parameter family of Hamilton operators, obtained via the method of self-adjoint extensions. One of the parameters, the value of the flux, corresponds to the Aharonov-Bohm effect; the other four parameters correspond to the strength of a singular potential barrier. The spectrum and eigenstates are computed and the scattering problem is solved.

19 pages, Latex

Cited by in corpus (46)

• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background
• Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field
• Quantum mechanics of a free particle on a pointed plane revisited
• On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation
• Quantum motion of a point particle in the presence of the Aharonov--Bohm potential in curved space
• Induced vacuum current and magnetic field in the background of a cosmic string
• Mathematical justification of the Aharonov-Bohm hamiltonian
• Spectra of soft ring graphs
• On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field
• Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
• Zero modes in a system of Aharonov-Bohm fluxes
• Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field
• Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin
• Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Magnetic Perturbations of Anyonic and Aharonov-Bohm Schrödinger Operators
• ADHM Construction of Instantons on the Torus
• Levinson's theorem and higher degree traces for Aharonov-Bohm operators
• Aharonov-Bohm effect on the Poincaré disk
• On the Pauli operator for the Aharonov-Bohm effect with two solenoids
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings
• A new version of the Aharonov-Bohm effect
• Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential
• Electron trapping by a current vortex
• Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Self-adjointness in Quantum Mechanics: a pedagogical path
• Semiclassical limit for almost fermionic anyons
• Diffraction of the Aharonov-Bohm Hamiltonian
• The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
• Quadratic forms for Aharonov-Bohm Hamiltonians
• Two-particle scattering theory for anyons
• Results on the Aharonov-Bohm effect without contact with the solenoid
• Differential cross section for Aharonov--Bohm effect with non standard boundary conditions
• The Aharonov--Bohm effect in scattering theory
• Reduction by symmetries in singular quantum-mechanical problems: general scheme and application to Aharonov-Bohm model
• Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications
• Deficiency indices for singular magnetic Schrödinger operators
• Bose-Einstein condensation in the presence of an impurity
• Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition
• Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)
• Several remarks on ``Comments'' by A. Moroz