Aharonov-Bohm Effect with $δ$--type Interaction

  title={Aharonov-Bohm Effect with \$$\delta$\$--type Interaction},
  author={L. Da̧browski and P. Stov{\'i}cek},
  journal={Journal of Mathematical Physics},
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. 
A New Version of the Aharonov–Bohm Effect
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 particleExpand
On the Pauli operator for the Aharonov–Bohm effect with two solenoids
We consider a spin-1/2 charged particle in the plane under the influence of two idealized Aharonov–Bohm fluxes. We show that the Pauli operator as a differential operator is defined by appropriateExpand
Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential
The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming fromExpand
Aharonov-Bohm effect on the Poincaré disk
We consider formal quantum Hamiltonian of a charged particle on the Poincare disk in the presence of an Aharonov-Bohm magnetic vortex and a uniform magnetic field. It is shown that this HamiltonianExpand
von Neumann Quantization of Aharonov-Bohm Operator with δ Interaction: Scattering Theory, Spectral and Resonance Properties
Abstract Using the theory of self-adjoint extensions, we study the interaction model formally given by the Hamiltonian Hα + V (r), where Hα is the Aharonov-Bohm Hamiltonian and V (r) is the δ-typeExpand
Finite correction to Aharonov-Bohm scattering by a contact potential
Abstract.We study the influence of a contact (or delta) potential on the Aharonov-Bohm scattering of nonrelativistic particles. In general the contact potential has no effect on the scattering asExpand
Aharonov–Bohm Effect in Resonances of Magnetic Schrödinger Operators with Potentials with Supports at Large Separation
Vector potentials are known to have a direct significance to quantum particles moving in the magnetic field. This is called the Aharonov–Bohm effect and is known as one of the most remarkable quantumExpand
We study zero modes of two-dimensional Pauli operators with Aharonov–Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also considerExpand
Aharonov–Bohm effect in scattering by a chain of point‐like magnetic fields
According to the Aharonov–Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by severalExpand
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
Two different self-adjoint Pauli extensions describing a spin-1/2 two-dimensional quantum system with singular magnetic field are studied. An Aharonov-Casher type formula is proved for the maximalExpand


Can elementary quantum mechanics explain the Aharonov–Bohm effect?
It is shown that a satisfactory treatment of the Aharonov–Bohm problem requires no departure from the basic principles of ordinary quantum mechanics, a fact not entirely clear in the literature. TheExpand
Exact Aharonov-Bohm wavefunction obtained by applying Dirac's magnetic phase factor
A solution of Schrodinger's equation for a particle in a magnetic field B can be obtained from the wavefunction when B=0 by Dirac's prescription of multiplication by a phase factor. But this solutionExpand
Aharonov–Bohm scattering and the velocity operator
It is shown that the existence of Aharonov–Bohm scattering depends upon the criteria used for establishing the stationary states. If one applies Pauli’s criterion, there is no scattering. It is shownExpand
Significance of Electromagnetic Potentials in the Quantum Theory
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there existExpand
Point interactions in two diemsions: Basic properties, approximations and applications to solid state physics.
On etudie rigoureusement l'operateur de Schrodinger formellement donne par H=−Δ−μδ(•−y) dans L 2 (R 2 ) et on montre comment l'approcher en termes d'hamiltoniens a courte portee transformesExpand
The Aharonov-Bohm e ect and scattering theory
Auxiliary cover means for temporarily replacing cover of diesel engine governor is disclosed. Cover has sealed passage which allows access to governor adjustment means while governor containsExpand
Matrices de Diffusion pour l'Opérateur de Schrödinger en Présence d'un Champ Magnétique. Phénomène de Aharonov-Bohm¶Erratum: Annales I.H.P. Vol. 61, No. 3, 1994
Dans cet article, nous etudions les matrices de diffusion associees a un operateur de Schrodinger avec champ magnetique a longue portee. Nous estimons la singularite de l'amplitude de diffusion surExpand
On nonlocal point interactions in one, two, and three dimensions
Three characterizations of all self‐adjoint extensions of the Laplacian in one, two, and three dimensions are discussed.
Tables of Integral Transforms (Bateman Manuscript Project)
  • Tables of Integral Transforms (Bateman Manuscript Project)
  • 1954
Scattering on a finite chain of vertices, Duke Math
  • J
  • 1994