Related papers: Analytic study of conformable Schrodinger equation…
The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are…
New approximate analytical solutions have been obtained for the conformable fractional collective Bohr Hamiltonian suitable for triaxial nuclei, with the harmonic oscillator in {\gamma}-part of the collective potential and different…
In this article and beginning with the Dirac solution to the Hydrogen atom in its ground state, the exact results corresponding to the expectation value of the distance of the electron to the proton and the maximum probability distance are…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…
Diffusion in heterogeneous energy and diffusivity landscapes is widespread in biological systems. However, solving the Langevin equation in such environments introduces ambiguity due to the interpretation parameter $\alpha$, which depends…
We present a new 3D SPH code which solves the general relativistic field + hydrodynamics equations in the conformally flat approximation. Several test cases are considered to test different aspects of the code. We finally apply then the…
A theoretical description of IR spectroscopy data for a hydrogen bond (HB) is constructed on the base of trigonometric double-well potential for which an exact analytic solution of the one-dimensional Schr\"odinger equation (SE) is…
The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated…
We solve the problem of a neutral atom interacting with a charged wire, giving rise to an attractive 1/r^2 potential in two dimensions. We show how a suitable average over all possible self-adjoint extensions of the radial Schroedinger…
The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential $\lambda z^2$ is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical…
A few approximate schemes to solve the Hedin equations self-consistently introduced in (Phys. Rev. B 94, 155101 (2016)) are explored and tested for the 3D electron gas at metallic densities. We calculate one electron spectra, dielectric…
This paper calculates the quantized energy levels of the hydrogen atom, using a metaplectic-c prequantization bundle and a definition of a quantized energy level that was introduced by the author in a previous paper. The calculation makes…
A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the…
A numerical method of solving the one-dimensional Schrodinger equation for the regular and irregular continuum states using the phase-amplitude representation is presented. Our solution acquires the correct Dirac-delta normalization by…
We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for…
Resonant nuclear reactions are a powerful tool for the determination of the amount and profile of hydrogen in thin layers of material. Usually, this tool requires the use of a standard of well-known composition. The present work, by…
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a…