Related papers: Majorana solution of the Thomas-Fermi equation

We analyse the linear confinement of a Majorana fermion in $\left(1+1\right)$-dimensions. We show that the Dirac equation can be solved analytically. Besides, we show that the spectrum of energy is discrete, however, the energy levels are…

We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd…

Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…

In this article, we present an iterative method to find simple roots of nonlinear equations, that is, to solving an equation of the form $f(x) = 0$. Different from Newton's method, the method we purpose do not require evaluation of…

The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be…

In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic…

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…

In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian…

We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with…

Integrals arising in the Thomas-Fermi (TF) theory of atomic structure and which contain logarithms of the Airy functions have been expressed in terms of the incomplete Bell polynomials. In keeping with the spirit of TF theory closed forms…

Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires…

A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…

Using the test-particle method, we solve numerically the Boltzmann equation for an ultra-cold gas of trapped fermions with realistic particle number and trap geometry in the normal phase. We include a mean-field potential and in-medium…

We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical…

A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…

We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…

We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…

An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can…

Fundamental solution of Fokker - Planck equation is built by means of the Fourier transform method. The result is checked by direct calculation. Changes: missed factor in (29), (30), corrected (31), (35), removed former (36), added…