Related papers: On the Hydrogen Atom via Wigner-Heisenberg Algebra
We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. It is presented a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture $ [x,p_{x}]=…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
We derive in a straightforward way the spectrum of a hydrogen atom in a strong magnetic field.
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 define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac…
We calculate atom-photon resonances in the Wigner-Weisskopf model, admitting two photons and choosing a particular coupling function. We also present a rough description of the set of resonances in a model for a three-level atom coupled to…
The Kustaanheimo-Stiefel transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
We present a scheme of the high-precise three-dimensional (3D) localization by the measurement of the atomic-level population. The scheme is applied to a four-level tripod-type atom coupled by three strong standing waves and a probe running…
We construct the $\mathcal{N}=8$ supersymmetric mechanics with potential term whose configuration space is the special K\"ahler manifold of rigid type and show that it can be viewed as the K\"ahler counterpart of $\mathcal{N}=4$ mechanics…
We investigate the classical dynamics of a Rydberg hydrogen atom near the surface of a planar topological insulator. The system is described by a Hamiltonian consisting of the free-hydrogen part and the hydrogen-surface potential. The…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no…
A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori…
To describe a relativistic hydrogen atom we used the Poincare-covariant model of a two particle system with gauge invariant potential. The kernel of the radial integral equation is obtained which describes a system of two fermions with…
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal $R$-matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum…
Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be…
The quantum algebra of observables of the massive closed bosonic string in 1+3 dimensions has been developed so far in the rest frame of the string. In this paper a method to write this algebra in a manifestly Lorentz covariant form is…
In this paper we will realize the polynomial Heisenberg algebras through the harmonic oscillator. We are going to construct then the Barut-Girardello coherent states, which coincide with the so-called multiphoton coherent states, and we…
Lattice simulations of five-dimensional gauge theories on an orbifold revealed that there is spontaneous symmetry breaking. Some of the extra-dimensional components of the gauge field play the role of a Higgs field and some of the…