Related papers: Two-dimensional Hydrogen-like Atom in a Constant M…
Several problems in mathematical physics relating to excitons in two dimensions are considered. First, a fascinating numerical result from a theoretical treatment of screened excitons stimulates a re-evaluation of the familiar…
The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.…
Herein, we present analytical solutions for the electronic energy eigenvalues of the hydrogen molecular ion H2+, namely the one-electron two-fixed-center problem. These are given for the homonuclear case for the countable infinity of…
The linear Stark effect for the first excited state of the hydrogen atom shows that, in the unperturbed states, the atom has a permanent electric dipole moment (EDM) of magnitude 3eao (ao is Bohr radius). The EDM is not induce by the…
The motion of a multi-electronic atom in an external electro-magnetic field is reconsidered. We prove that according to classical mechanics and electrodynamics, the assumption that the interaction with the magnetic field is described by…
The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated…
When a hydrogen-like atom is treated as a two dimensional system whose configuration space is multiply connected, then in order to obtain the same energy spectrum as in the Bohr model the angular momentum must be half-integral.
The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of…
It is shown that both the electric and magnetic dipole moment vectors of hydrogen atom in the excited states with wave function $$ u_n^{(\pm)} = {1\over\sqrt 2} [R_{n,n-1}(r) Y_{n-1,\pm (n-2)}(\theta\phi) \pm R_{n,n-2}(r) Y_{n-2,\pm…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
The Hamiltonian of a pure hydrogen atom possesses the SO(4) symmetry group generated by the integrals of motion: the angular momentum and the Runge-Lenz vector. The pure hydrogen atom is a supersymmetric and superintegrable system, since…
In the first part of the present work, the correction to photon emission rate of an oscillating two-level atom in the presence of electromagnetic quantum vacuum field has been investigated for two different configurations: (i) Atom is…
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis…
We derive in a straightforward way the spectrum of a hydrogen atom in a strong magnetic field.
We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the…
Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the…
Analytical approximations are constructed for binding energies of hydrogen atoms arbitrarily moving in magnetic fields 7\times10^{11} G to 2\times10^{13} G, typical of magnetic neutron stars.
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
Hydrodynamics of plasma in the random magnetic field is considered, which is characterized by the second moment of magnetic induction. Equations of ideal magnetic hydrodynamics in such field are received for an adiabatic process. It is…