Alternative relativistic formulation of linear spectrum of hydrogen-like systems

The article describes the possibility of describing the electronic structure of the simplest atomic systems within corpuscular physics theory. The proposed method allows to derive the Rydberg frequency constant without using quantum Bohr postulates. Adequate results of the same type of calculation of the energy levels of the first five chemical elements that are in the maximum degree of ionization are presented. The results of the paper can increase the accuracy and reduce the computational complexity of models of quantum processes and phenomena. This, in turn, may allow one to develop more efficient models and algorithms for controlling such systems.

Canonical relativistic formulation to calculate the Casimir force four-vector on anisotropic conductor polarizable and magnetizable media

A canonical relativistic formulation to calculate the Casimir force four-vector exerted on anisotropic conductor polarizable and magnetizable media is provided. The anisotropic conductor polarizable and magnetizable medium is modeled by a continuum collection of the antisymmetric tensor fields of the second rank and a continuum collection of the vector fields in Minkowski spacetime. The collection of the antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The collection of the vector fields describes the conductivity property of the medium. The quantum relativistic wave equation of the four-vector potential of the electromagnetic field is solved using an iteration method. According to the conservation principle of the energy–momentum four-vector and using of the energy–momentum tensors of the relativistic dynamical fields, contained in the theory, the Casimir force four-vector on the anisotropic conductor polarizable and magnetizable medium is obtained. The Casimir force four-vector is obtained in terms of the relativistic dynamical fields, contained in the theory and the coupling tensors that couple the electromagnetic field to the anisotropic conductor polarizable and magnetizable medium. The Casimir force four-vector exerted on the medium is calculated in the vacuum state of the total system. As a special case, the formulation is applied to a multilayer medium. The tangential component of the Casimir force exerted on a multilayer medium vanish when the anisotropic conductor polarizable and magnetizable medium is converted to an isotropic one.