We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the correct boundary conditions is not independent of the physical structure of the proton. Under the physically reasonable assumption that the finite size and struc...

Two efficient spectral-element methods, based on Legendre and Laguerre polynomials respectively, are derived for direct approximation of the electronic Schrödinger equation in one spatial dimension. Compared to existing literatures, a spectral-element approach is used to treat the singularity in nucleus-electron Coulomb potential, and with the help of Slater determinant, special basis functions...

A model is proposed to describe a transition from a charged black hole of mass M and charge Q to one of mass M and charge Q. The basic equations are derived from the non-vacuum Einstein field equations sourced by the Coulomb field and by a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace of the energy-momentum tensor prevents the formation of a naked ...

We consider the spectral problem for a perturbed two-dimensional oscillator. The role of perturbation is played by an integral Hartree type nonlinearity with self-action potential depending on distance between points and possessing Coulomb singularity. find asymptotic eigenvalues eigenfunctions near boundaries clusters appearing unperturbed operator. we construct expansion circle, where solutio...

The magnetic charge concept is further developed to define the vibrational motion of a charged particle moving in ether/dark matter. angular momentum resulting derived be ħ/2 at all velocities. also provides additional justification for Coulomb and gravitational forces not having singularity. Additional insights into antimatter composition annihilation are developed.

The Haft Saravan area is located in 90 km SE Arak in the central Iran. This area is a part of Malyer-Isfahan metallogenic belt. The article's objective is determining the most suitable method for identifying mineralized zones using original singularity and weighted singularity methods in three-dimensional space. In weighted singularity method, mineralized zones have a greater volume relative to...

We study the quark-antiquark interaction in the large N limit of the superconformal field theory on D-3branes at a Calabi-Yau conical singularity. We compute the Wilson loop in the AdS5 × T 11 supergravity background for the SU(2N) × SU(2N) theory. We also calculate the Wilson loop for the Higgs phase where the gauge group is broken to SU(N) × SU(N) × SUD(N). This corresponds to a two center co...

We continue the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries. This classification was begun in [1] where singularities corresponding to curves of the form y2 = x6 with a fixed canonical basis of holomorphic one forms were analyzed. Here we perform the analysis for the y2 = x5 type singularities. (The final maximal singularity type, y2 = x3(x − 1)3, will ...

We develop a systematic method to describe the moduli space of vacua of four dimensional N = 2 class S theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin’s equations obtained from twisted compactifi...