Related papers: The hydrogen atom in $D=3-2\epsilon$ dimensions
Highly accurate measurements of quantum level energies in molecular systems provide a test ground for new physics, as such effects could manifest themselves as minute shifts in the quantum level structures of atoms and molecules. For 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…
We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit,…
The nonrelativistic energy together with relativistic and quantum electrodynamic corrections for all the molecular hydrogen isotopologues (D$_2$, T$_2$, HD, HT, DT) were evaluated without expansion in the electron-nucleus mass ratio. The…
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 present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
We obtain the specific heat in the third constraint scenario for a canonical ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The canonical ensemble of N particles in D dimensions is well-defined for the choice of…
Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an…
Recurrence relations of perturbation theory for hydrogen ground state are obtained. With their aid polarizabilities in constant perpendicular electric and magnetic fields are computed up to 80th order. The high orders asymptotic is compared…
Energy levels of neutral atoms have been re-examined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies…
With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions…
In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
We derive the wave function for N-dimensional hydrogen atom in the momentum representation with the phase factor using the generating function method and Hankel's integral.
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…
In the present work, we predict the existence of new types of hydrogenlike matter, including hydrogenlike atoms ($\pi^+e^-$, $K^+e^-$, $D^+e^-$), hydrogenlike molecular ions ($\pi^+\pi^+e^-$, $K^+K^+e^-$, $D^+D^+e^-$) and hydrogenlike…
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the…
The impact of 1GeV/Nucleon U92+ projectiles against atomic hydrogen is studied by direct numerical resolution of the time-dependent wave equation for the atomic electron on a three-dimensional Cartesian lattice. We employ the fully…
We study perturbative behavior of free energies on a d-dimensional sphere S^d for theories with marginal interactions. The free energies are interpreted as the "dilaton effective action" with the dilaton having a nontrivial background…
A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential $\Delta…