Related papers: The Hydrogen Atom within a pseudo-complex Quantum …
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent…
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…
We study electroweak interactions in the multiscale theory with $q$-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale $t_*$,…
We present a brief historical introduction to the motivations behind quantum mechanics and quantum field theory on noncommutative spacetime and provide an insightful technique, readily accessible to the undergraduate student, to examine the…
We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation.…
The two-loop self-energy correction to the ground state Lamb shift is calculated for hydrogen-like ions with the nuclear charge Z=10-30 without any expansion in the binding field of the nucleus. A calculational technique is reported for…
We investigate black-body induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure and…
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two…
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…
Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this paper, we comment on…
The nonrelativistic hydrogen atom in $D=3-2\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the…
The screening of a Coulomb potential by superstrong magnetic field is studied. Its influence on the spectrum of a hydrogen atom is determined.
We present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon and Dirac equations in a non-commutative space-time up to…
Recently it was shown that classical "relativistic" particle dynamics was implicit in physics going back to Maxwell. The demonstration utilized a simple modification of a 1906 thought experiment by which Einstein established the mass…
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar…
We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for…
We consider possible tests of the Einstein Equivalence Principle for physical systems in which quantum-mechanical vacuum energies cannot be neglected. Specific tests include a search for the manifestation of non-metric effects in Lamb-shift…
In quantum gravity it is generally thought that a modified commutator of the form $[{\hat x}, {\hat p}] = i \hbar (1 + \beta p^2)$ is sufficient to give rise to a minimum length scale. We test this assumption and find that different pairs…