相关论文: Mathematical Structure of Relativistic Coulomb Int…

We evaluate the matrix elements <Or^{p}>, where O ={1, \beta, i\alpha n \beta} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of the…

With the help of computer algebra we study the diagonal matrix elements <Or^p>, where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem. Using…

Recently we have evaluated the matrix elements $<Or^{p}>$,$ where $O$ $={1,\beta, i\mathbf{\alpha n}\beta} $ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb…

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring…

The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…

Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…

Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…

We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…

General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…

The correspondence between commutative rings of ordinary differential operators and algebraic curves has been extensively and deeply studied since the seminal works of Burchnall-Chaundy in 1923. This paper is an overview of recent…

We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic integrable many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interaction. Using…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

The Hamiltonian of the radial Coulomb Klein-Gordon and second order Dirac equations are shown to possess an infinite symmetric tridiagonal matrix structure on the relativistic Coulomb Sturmian basis. This allows us to give an analytic…

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated…

We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_{\omega,\lambda}:=\begin{bmatrix}-\frac{\lambda+\omega}{x}&-\partial_x \\ \partial_x & -\frac{\lambda-\omega}{x}\end{bmatrix}$.…

A classification of commutative integral domains consisting of ordinary differential operators with matrix coefficients is established in terms of morphisms between algebraic curves.

It is shown that the rich algebraic structure of the standard $d$-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so($d+1$,2) dynamical algebra generators of the…

A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in…