Related papers: The hydrogen atom as relativistic bound system
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
Potential energy curves for excited leptonic states of the helium-antihydrogen system are calculated within Ritz' variational approach. An explicitly correlated ansatz for the leptonic wave function is employed describing accurately the…
In Part one of this Paper a hypothesis is forwarded of the electron charge in an atom existing in a distributed form. To check it by methods of electrodynamics and mechanics (without invoking the formalism of quantum mechanics and the…
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of mass $m$ and charge $e$. This system forms…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We study the electrical susceptibility of a hydrogen gas at equilibrium, partially ionized by thermal excitations. The gas is described as a quantum plasma of point protons and electrons, interacting via the Coulomb potential. Using the…
The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic…
We studied the hydrogen atom as a system of two quantum particles in different confinement conditions; a spherical-impenetrable-wall cavity and a fullerene molecule cage. The motion is referred to the center of spherical cavities, and the…
An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigen-states of the Stark-Hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an…
We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential.…
The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
We demonstrate that energy levels of excited states in a hydrogenic system consisting of an arbitrary nucleus and an antiproton can be calculated within the framework of nonrelativistic quantum electrodynamics, even for a large nuclear…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
The problem of proton-antiproton motion in the ${\rm H}$--${\rm \bar{H}}$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
The methodology based on the association of the Variational Method with Supersymmetric Quantum Mechanics is used to evaluate the energy states of the confined hydrogen atom.
Recent experiments on the laser-induced resonant annihilation provide a precise measurement of transition energies of antiprotonic helium atoms. Relativistic corrections of an order of $\alpha ^2$ to the pure Coulomb interaction will be…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…