Related papers: Hydrogen atom bound states whose spectral measures…
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…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
Theoretical energy levels of the $n = 1$ and $n = 2$ states of hydrogenlike atoms with the nuclear charge numbers $1 \le Z \le 110$ are tabulated. The tabulation is based on ab initio quantum electrodynamical calculations performed to all…
A long-distance effective theory of hydrogen-like atoms, dubbed the relativistic Ritz approach was recently introduced and some its theoretical consequences were explored. In this article, the relativistic Ritz approach is used to fit…
In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schr\"odinger equation in…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
We show that dynamical localization for excited hydrogen atoms in magnetic and microwave fields takes place at quite low microwave frequency much lower than the Kepler frequency. The estimates of localization length are given for different…
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated…
Stationary states of non-interacting electrons on a Koch fractal are investigated within a tight binding approach. It is observed that if a hierarchically long range hopping is allowed, a suitable correlation between the parameters defining…
We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H\"older…
Usually the ions in solid are in the positive oxidation states or in the negative oxidation state depending upon the chemical environment. It is highly unusual for an ion having both positive as well as negative oxidation state in a…
We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of…
The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the…
We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…
The ground and excited vibrational states for the three hydrogen isotopes on the Pd(111) surface have been calculated. Notable features of these states are the high degree of anharmonicity, which is most prominently seen in the weak…
In this paper the N=2 supersymmetric extension of the Schroedinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the…
As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most…
The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…
We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give exponentially decreasing lower bounds to rho~ in the case…