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Continuum states of the Dirac equation are calculated numerically for the electrostatic field generated by the charge distribution of an atomic nucleus. The behavior of the wave functions of an incoming electron with a given asymptotic…
An optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems is proposed. The variational method is based on an expansion in coherent states that leads to a dramatic truncation in the phonon space.…
We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The Canonical Function Method (CFM) is a powerful accurate and fast method that solves the Schr\"{o}dinger equation for the eigenvalues directly without having to evaluate the eigenfunctions. Its versatility allows to solve several types of…
We employ the familiar canonical quantization procedure in a given cosmological setting to argue that it is equivalent to and results in the same physical picture if one considers the deformation of the phase-space instead. To show this we…
The non-local van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be…
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-\Delta u+ \alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave-function correlated and…
One of the most important open challenges in modern Kohn-Sham (KS) density-functional theory (DFT) is the correct treatment of fractional electron charges and spins. Approximate exchange-correlation (XC) functionals struggle to do this in a…
The moving coframe method is applied to solve the local equivalence problem for the class of nonlinear wave equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…
In this article, a modification of the rapidly convergent approximation method is proposed to solve a coupled Korteweg-de Vries equations with conformable derivative that govern shallow-water waves. Based on the Leibniz and chain rule of…
Nonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electron-nucleus…
This paper proposes a method for estimating and detecting optical signals in practical photon-counting receivers. There are two important aspects of non-perfect photon-counting receivers, namely, (i) dead time which results in blocking…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…