Related papers: The Calculation of Matrix Elements in Relativistic…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor-coefficients of the…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels…
The intention of this paper is to provide solutions to commutative relations relevant to calculations regarding the hydrogen atom (or similar monoelectronic systems). Though exact solutions exist to these systems, the value to approximation…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the…
The Matrix Element Method is a promising multi-variate analysis tool which offers an optimal approach to compare theory and experiment according to the Neyman-Pearson lemma. However, until recently its usage has been limited by the fact…
We assume that all quark and lepton $3 \times 3$ mass matrices which appear in the standard model lagrangian (after spontaneous symmetry breaking) with neutrinos treated as Dirac patricles have the triangular form. Such matrices have not…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
A consistent analytical approach for calculation of the quasiclassical radial dipole matrix elements in the momentum and coordinate representations is presented. Very simple but relatively precise expressions for the matrix elements are…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
Magnetic reconnection -- a fundamental plasma physics process, where magnetic field lines of opposite polarity annihilate -- is invoked in astrophysical plasmas as a powerful mechanism of nonthermal particle acceleration, able to explain…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for…
We consider the Nuclear Modification Ratios in heavy ion collisions, R_CP and R_AA, in the region of intermediate transverse momentum, and study the dependency upon the constituent quark composition of the observed hadron. Adopting a two…
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an objective extra space dimension. "Particle"…
We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue…
We discuss the computation of two-body matrix elements from the Argonne $v_{18}$ interaction. The matrix elements calculation is presented both in particle-particle and in particle-hole angular momentum coupling. The procedures developed…