Related papers: On Aharonov-Casher bound states
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found…
In this paper, we study the influence of the Aharonov-Casher effect [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984).] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the…
The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\"odinger-Pauli…
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $\mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous…
In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at…
In this manuscript, we investigate the influence of the Aharonov-Casher effect on the generalized Dirac oscillator containing the Coulomb-type potential function related to a relativistic neutral particle having a permanent magnetic dipole…
The solution of the Breit equation with an instantaneous potential for the case of two spin-1/2 particles in a pseudoscalar bound state is considered. This is then applied to charmonium using a potential of the Cornell type. The masses of…
Solutions to the Dirac equation are constructed for a massless charged fermion in Coulomb and Aharonov--Bohm potentials in 2+1 dimensions. The Dirac Hamiltonian on this background is singular and needs a one-parameter self-adjoint…
We analyze recently published results about the Aharonov-Bohm effect for bound states from the interaction of the magnetic quadrupole moment of a neutral particle with axial fields. We show that the eigenvalues obtained by the authors from…
In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially…
Magnetic Aharonov-Bohm effect (AB effect) was studied in hundreds of papers starting with the seminal paper of Aharonov and Bohm [AB] published in 1959. We give a new proof of the magnetic Aharonov-Bohm effect without using the scattering…
We study a planar magnetic Schr\"odinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on…
The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\otimes \epsilon$…
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the…
The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov--Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the…
The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum,…
We obtain exact solutions to the Dirac equation and the relevant binding energies in the combined Aharonov--Bohm--Coulomb potential in 2+1 dimensions. By means of solutions obtained the quantum Aharonov--Bohm effect is studied for free and…
A field-interaction scheme is introduced for describing the Aharonov-Bohm effect, fully consistent with the principle of relativity. Our theory is based on the fact that local field interactions are present even when a particle moves only…
In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded planar domain. We establish a sharp relation between the rate of…