Relativistic ro‐vibrational feature of electron in Bohr's orbits of hydrogen‐like atoms in Heisenberg picture

Abstract

The relativistic effects have been widely reported to affect the chemical and physical properties of the heavy elements such as lanthanides (57≤z≤71), actinides (89≤z≤103), and transactinides (z≥104). This effect is definitely weakened by reducing the atomic number z 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) Hitalicvibitalicrel is expanded as a power series of harmonic oscillator Hamiltonian H0 for the first time. By applying the first‐order RVH (correct to H0) 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 z beyond z≈20. 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.