Volume 19: Pages 638-648, 2006
On the Special Theory of Relativity, the Mechanics of a Radiating Charged Point Particle (Electron), and the Lamb Shift in the Hydrogen Atom
Dimitar G. Germanov 1
1Department of Physics, Higher Institute of Transport Engineering, Todor Kableshkov, Sofia 1574, Bulgaria
The initial formulation of the special theory of relativity (STR) for the movement of an electron in an electromagnetic field is used. The acceleration of the electron is considered by taking into account the work of the field forces, which is converted into an energy of the electron's own electromagnetic field (quasi‐stationary and wave‐field radiation). The STR considers only the work of the field forces, which is entirely converted into kinetic energy. In this sense the STR considers an electron that does not create its own electromagnetic field. We show that, without changing the basic principles of the STR (space‐time relationships that fit the Lorentz transformations), and taking into consideration the work of the field forces for creating an electromagnetic field of the electron, the formula that gives the relationship between the total energy of the electron and its linear momentum is different from that of the STR. The difference is that this relationship also includes the energy of the electromagnetic field of the electron created by its motion. The application of our formula to the hydrogen atom yields two equations. The first one is the Klein‐Gordon equation. By taking into account the spin‐orbital interaction of the electron, the solution of this equation gives the fine structure of the hydrogen atom. The second equation gives an account of both the energy of the electron's own electromagnetic field and the fluctuations of the energy of the electron. From it we obtain the shift of the levels with the same quantum numbers n and j. For the frequency of the transition 2S1/2 − 2P1/2 (Lamb shift) we obtain 1057.8406(6) MHz (L(2S) = 1045.0064 MHz and L(2P) = −12.8342 MHz). It is evident that this value coincides very well with the experimental one. From both equations and the experimental value of the transition 2S − 1S, for the Lamb shift of level 1S we obtain the value L(1S) = 8172.834 MHz. This value also perfectly coincides with the experimental one L(1S) = 8172.837(22) MHz.
Keywords: special theory of relativity, quantum mechanics, Lamb shift in hydrogen atom
Received: June 6, 2005; Published Online: December 15, 2008