Related papers: Two charges on plane in a magnetic field: II. Movi…
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field $B$ perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal…
The quantum mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field $B$ perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for…
The $He^+$ ion on a plane subject to a constant magnetic field $B$ perpendicular to the plane is considered taking into account the finite nuclear mass. Factorization of eigenfunctions permits to reduce the four-dimensional problem to…
A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is considered. Special "superintegrable" trajectories (circular and linear) for which the…
As a generalization and extension of JMP 54 (2013) 022901, the classical dynamics of three non-relativistic Coulomb charges $(e_1, m_1)$, $(e_2, m_2)$ and $(e_3, m_3)$ on the plane placed in a constant magnetic field perpendicular to the…
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of…
Binary collisions between charged particles in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
The 2-dimensional charge transport with parallel (in plane) magnetic field is considered from the physical and mathematical point of view. To this end, we start with the magnetic field parallel to the plane of charge transport, in sharp…
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…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
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…
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…