Related papers: Reference potential approach to the quantum-mechan…
The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…
We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the…
A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…
This work employs the spectral reconstruction approach of Ref. [1] to determine an inclusive rate in the $1+1$ dimensional O(3) non-linear $\sigma$-model, analogous to the QCD part of ${e}^+{e}^- \rightarrow \rm {hadrons}$. The Euclidean…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a…
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of…
In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for $q$-analogue of the heat equation. As an over-determination condition we have used integral type condition on…
This paper investigates the problem of reconstructing a random source from statistical phaseless data for the two-dimensional Helmholtz equation. The major challenge of this problem is non-uniqueness, which we overcome through a reference…
We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
The screened quasi-relativistic potential is used for describing spin-orbit splitting in $^{3}P_{J}$ waves of quark-antiquark system. Fermi-Breit equation is solved numerically in configuration interaction approximation. This approximation…
Reference potential approach (RPA) is successful in obtaining inverse potentials for weakly bound diatomic molecules using Morse function. In this work, our goal is to construct inverse potentials for all available l-channels of…
By using the \emph{Rydberg--Klein--Rees} (RKR) formulas to solve the inverse Schr\"{o}dinger problem, we found a confining bottom-up potential from a given eigenvalue spectrum. To illustrate this methodology, we consider the vector meson…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…