Related papers: Finite-gap potential, Heun's differential equation…
We study the Weyl-type solutions of the differential system with a singularity $y'-x^{-1}Ay-q(x)y=\rho By$ in the case of integrable potential $q(\cdot)$.
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…
In this article we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of Quantum Field Theory in curved space-times. In particular, we relate the separated radial part of a massive Dirac equation…
A finite difference method (FDM) applicable to a two dimensional (2D) quantum dot was developed as a non-conventional approach to the theoretical understandings of quantum devices. This method can be applied to a realistic potential with an…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
In the present work, we propose to investigate the second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting applications of the results presented here are also discussed.
In this paper we show that the one-dimensional Schr\"odinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schr\"odinger equation with a finite-gap potential, the metric and geodesics are…
The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become a basic tool for the study of electronic structure of matter. In this article, we study the Hohenberg-Kohn theorem for a class of external…
In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and…
For $(Q,W)$ a symmetric quiver with potential satisfying a K\"unneth-type condition, we construct (positive and negative) extensions of its K-theoretic Hall algebra which are bialgebras. In particular, there are bialgebra extensions of…
We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
We present some results in the analysis of non-compact differential equations on unbounded domains.
The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson structure on $T^*S^3$. This global description naturally leads…
In this rather popular paper we stress some basics of the theory and the huge amount of applications of the Heun functions, as well as the still existing basic unsolved problems. The point is to attract more attention to this modern…
A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved.…
We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain…
Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions.…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…