Related papers: Hydrogen atom bound states whose spectral measures…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
The Dirac equation is used to provide a relativistic calculation of the binding energy of a hydrogen-like atom confined within a penetrable spherical barrier. We take the potential to be Coulombic within the barrier and constant outside the…
This article presents a review of the most recent theoretical and experimental results in hydrogen. We particularly emphasize the methods used to deduce the Rydberg constant $R_\infty$ and we consider the prospects for future improvements…
Recently, spectroscopic and calorimetric observations of hydrogen plasmas and chemical reactions with them have been interpreted as evidence for the existence of electronic states of the hydrogen atom with a binding energy of more than 13.6…
The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a…
In this work, we investigate the bound state problem in one dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that, the flat band has significant effects on the bound states. For example, for Dirac delta potential…
We solve the bound state problem for the Hamiltonian with the spin-orbit and the Raman coupling included. The Hamiltonian is perturbed by a one-dimensional short-range potential V which describes the impurity scattering. In addition to the…
We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…
This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schr\"{o}dinger Equation and provides insights into its consequences. The study presents a General Solution for…
Probability of finding negative energy states in a hydrogen atom is decreased when the nucleus is extended. Reduced electron Compton wavelength is the characteristic size of the region around the nucleus where negative energy contributions…
The one dimensional Schroedinger hydrogen atom is an interesting mathematical and physical problem to study bound states, eigenfunctions and quantum degeneracy issues. This 1D physical system gave rise to some intriguing controversy over…
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 finite-basis, pair formulation of the Spectral Theory of chemical bonding is briefly surveyed. Solutions of the Born-Oppenheimer polyatomic Hamiltonian totally antisymmetric in electron exchange are obtained from diagonalization of an…
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…
The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac's equation is not square integrable. For this reason the…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
In this paper, the off-diagonal geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Increasing temperature tends to suppress the off-diagonal geometric phase, including 1-order and…
The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P,…
We study, in the multipolar coupling scheme, a uniformly accelerated multilevel hydrogen atom in interaction with the quantum electromagnetic field near a conducting boundary and separately calculate the contributions of the vacuum…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…