Relativistic quantum physics equation for number of electrons

J. Jahanpanah, Ali Vahedi, H . Khosrojerdi

Abstract The relativistic effects have been widely reported to affect the chemical and physical properties of the heavy elements such as lanthanides (), actinides (), and transactinides (). This effect is definitely weakened by reducing the atomic number in lighter elements such as hydrogen‐like atoms (HLAs). The aim of present paper is to investigate the relativistic effects of electron motion in Bohr orbits on the chemical and physical properties of HLAs. The theoretical model is based on the Heisenberg (rather than Schrodinger) picture where the relativistic vibrational Hamiltonian (RVH) is expanded as a power series of harmonic oscillator Hamiltonian for the first time. By applying the first‐order RVH (correct to ) to the Heisenberg equation, a pair of coupled equations is obtained for the relativistic position and linear momentum of electron. A simple comparison of the first‐order relativistic and nonrelativistic equations reveals that the relativistic natural frequency of an HLA (like entropy) is slowly raised by increasing beyond . In general, RVH plays a fundamental role because it specifies the temporal relativistic variations of position, velocity, and linear momentum of the oscillating electron. The results are finally verified by demonstrating energy conservation.

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

Mubarak Dirar Abd-Alla Yagoub, Mohammed El Idriss

Using generalized special relativistic energy-momentum relation the linear energymomentum Dirac relation was obtained. This equation was used to find Dirac generalized relativistic quantum equation. This equation was used to find the probability and the number of particles for each atomic energy level. The wave function found using this equation can give an expression for the number of electrons in each energy levels if the atomic radius is quantized and satisfy a certain relation.

T. P. Das

Claude Daviau

The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.

Eugene Paul Wigner