Related papers: $SO(4)$ Symmetry in Hydrogen Atom with Spin
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the Hydrogen atom are investigated. It is used standard Rayleigh-Schr\"odinger perturbation theory in order to obtain the corrections to the the ground…
In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
Hydrogen is the most abundant element in the universe. It is also the lightest and as such the most quantum of the elements, in the sense that quantum tunnelling, quantum delocalisation, and zero-point motion can be important. For practical…
It is shown the central field Dirac equation can be simplified through the use of real conjugate spinors to substitute for the upper and lower components of the bi-spinor eigensolutions. This substitution reduces the Dirac equation for the…
For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields.…
We study the energy conversion laws of the macroscopic harmonic $LC $ oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the…
New superintegrable systems are presented which, like the Hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One of them simulates a neutral fermion with non-trivial dipole moment, interacting with the external e.m. field.…
Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature…
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its…
We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
An emergent $\mathrm{SU}(4)$ symmetry discovered in the microscopic model for $d^1$ honeycomb materials [M.~G.~Yamada, M.~Oshikawa, and G.~Jackeli, Phys. Rev. Lett. \textbf{121}, 097201 (2018).] has enabled us to tailor exotic…
The nuclear spin, being much more isolated from the environment than its electronic counterpart, enables quantum experiments with prolonged coherence times and presents a gateway towards uncovering the intricate dynamics within an atom.…
We study a 5D bottom-up holographic model that is expected to describe the dynamics of the minimal composite Higgs model characterized by a $SO(5)\to SO(4)$ global symmetry breaking pattern. We assume that the fundamental degrees of freedom…
The Lorentz contraction of bound states in field theory is often appealed to in qualitative descriptions of high energy particle collisions. Surprisingly, the contraction has not been demonstrated explicitly even in simple cases such as 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…
New insights into our understanding of the semirelativistic excitation of atomic hydrogen by electronic impact have been made possible by combining the use of polarized electron beams and intense laser field. The paper reviews relativistic…
The hydrogen atom in weak external fields is a very accurate model for the multiphoton excitation of ultrastable high angular momentum Rydberg states, a process which classical mechanics describes with astonishing precision. In this paper…
The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically…