Related papers: Using a computer algebra system to simplify expres…
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is…
In this paper, a new efficient computational algorithm is presented for solving cyclic heptadiagonal linear systems based on using of heptadiagonal linear solver and Sherman-Morrison-Woodbury formula. The implementation of the algorithm…
Monogenic functions in the algebra of 5-dimensional spacetime have been used previously by the author as first principle in different areas of fundamental physics; the paper recovers that principle applying it to the hydrogen atom. The…
A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based…
Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
In this paper we introduce a new model for the quantum-mechanical system of the hydrogen atom. We start with a four-dimensional Lorentzian quadratic space $(V,q)$ and let $C \subset V$ be the corresponding cone. The Hilbert space of our…
We provide a detailed treatment of Weyl-Titchmarsh theory for half-lattice and full-lattice Cantero-Moral-Velazquez (CMV) operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions,…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of…
We present the application of the Schur-Weyl duality in the one-dimensional Hubbard model in the case of half-filled system of any numer of atoms. We replace the actions of the dual symmetric and unitary groups in the whole Hilbert space by…
A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.
We review the enveloping algebra of the 10 dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the…
The partial oxidation of methane was investigated using a self-stirred reactor under a wide range of operating conditions. The recation mechanism was determined by comparing ecperimental results with the results of simulations made using…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Small perturbations of the Jacobi matrix with weights \sqrt n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical…
Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition…