Related papers: Two charges on a plane in a magnetic field: hidden…
Starting with the premise that the electric charge associated with fundamental fermions (quarks and leptons) can, under certain circumstances, be appropriately represented as a real \emph{internal} 2-vector, the mathematical ``machinery''…
The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems…
The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. For example, Landau's solution for a particle moving…
Magnetically uncharged, magnetic linear response of the vacuum filled with arbitrarily combined constant electric and magnetic fields to an imposed static electric charge is found within general nonlinear electrodynamics. When the electric…
We investigate the properties of neutral and charged mesons in magnetic fields, from weak-field to strong-field regimes. To develop analytic insights, we employ a non-relativistic quark model with a confining potential of the harmonic…
The behavior of the electromagnetic field near a common edge of a resistive half-plane and a perfectly conducting wedge is investigated. The possible appearance besides power terms also of logarithmic functions in the field expansions at…
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr\"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator…
Experiments reveal that a confined electron system with two equally-populated layers at zero magnetic field can spontaneously break this symmetry through an interlayer charge transfer near the magnetic quantum limit. New fractional quantum…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent…
The classic image problem in electromagnetism involves a grounded infinite conducting plane and a point charge. The force of attraction between the point charge and the plane is identified using an equivalent-field picture of an image…
Coulomb effects on the edge states of a two dimensional electron gas in the presence of a high magnetic field are studied for different widths of the boundaries. Schr\"odinger and Poisson equations are selfconsistently solved in the integer…
Nonlinear Maxwell equations are written up to the third-power deviations from a constant-field background, valid within any local nonlinear electrodynamics including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear electric…
We consider a system of two interacting particles with like but unequal charges in a magnetic field in the planar geometry. We construct a complete basis of states compatible with both the axial symmetry and magnetic translations. The basis…
We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the north and south poles, and with…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
We discuss the occurence and properties of exact singular anyonic wave functions describing stationary states of two identical charged particles moving on a plane and under the influence of a perpendicular uniform magnetic field.