Related papers: $SO(4)$ Symmetry in Hydrogen Atom with Spin
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…
Starting from ${\cal N}=4$ SYM and using an appropriate Higgs mechanism we reconsider the construction of a scalar field theory non-minimally coupled to a Coulomb potential with a relativistic SO(4) symmetry and check for scalar field…
The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type hydrogen atom is connected to a four-dimensional…
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…
The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental…
The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex…
Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal…
Since the early days of quantum mechanics hydrogen, as the simplest of all atoms, has been studied or used to investigate new physics. In parallel, this knowledge leads to different applications, e.g. a spin filter to separate metastable…
The O(4) supersymmetry of the hydrogen atom is utilized to construct a complete basis using only the bound state wave functions. For a large class of perturbations, an expansion of the electron (exciton) wave function into such a complete…
Pauli first noticed the hidden SO(4) symmetry for the Hydrogen atom in the early stages of quantum mechanics [1]. Departing from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states…
In this paper we introduce a new model for the quantum-mechanical system of the hydrogen atom. We start with a four-dimensional Lorentzian quadratic space $(V,q)$ and let $C \subset V$ be the corresponding cone. The Hilbert space of our…
We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space ${\cal H}^p$ of pure $SU(2)_{2+1}$ lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms.…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times…
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…
The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the…
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving…