Related papers: $SO(4)$ Symmetry in Hydrogen Atom with Spin
We discuss how to construct a tight binding model Hamiltonan for the simplest possible solid, composed of hydrogen-like atoms. A single orbital per atom is not sufficient because the on-site electron-electron repulsion mixes in higher…
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a…
We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of…
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.
We introduce a simplified low-energy effective Lagrangian description of the phenomenology of heavy vector resonances in the minimal composite Higgs model, based on the coset SO(5)/SO(4), analysing in detail their interaction with lighter…
We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and…
Rovibrational transitions in the hydrogen and antihydrogen molecular ions $H_2^+$ and $\overline{H}_2^-$ offer the possibility of testing Lorentz and CPT symmetry to extremely high precision, in principle attaining $O(10^{-17})$. In this…
We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics…
A notion of quantization is proposed that is independent of the original statistical interpretation of the distribution of energy in a photon gas or of the quantization of angular momentum in hydrogen atom. Such a procedutre implies the…
The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in…
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…
Many large scale numerical simulations of astrophysical plasmas must also reproduce the hydrogen ionization and the resulting emission spectrum, in some cases quite accurately. We describe a compact model hydrogen atom that can be readily…
The pseudo-SU(3) model is used to describe the low-energy spectra as well as $E2$ and $M1$ transition strengths in $^{158}$Gd. The Hamiltonian includes spherical single-particle energies, the quadrupole-quadrupole and proton and neutron…
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schr\"odinger equation…
We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$. The additional spatial…
We have constructed a set of non-Hermitian operators that satisfy the commutation relations of the SO(3)-Lie algebra. It is shown that this operators generate rotations in the configuration space and not in the momentum space but in a…
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…
Hedin's equations for the electron self-energy and the vertex were originally derived for a many-electron system with Coulomb interaction. In recent years it has been increasingly recognized that spin interactions can play a major role in…