  In order to extend the limits of classical theory application in the
microworld some weak generalization of Maxwell electrodynamics is suggested. It
is shown that slightly generalized classical Maxwell electrodynamics can
describe the intraatomic phenomena with the same success as relativistic
quantum mechanics can do. Group-theoretical grounds for the description of
fermionic states by bosonic system are presented briefly. The advantages of
generalized electrodynamics in intraatomic region in comparison with standard
Maxwell electrodynamics are demonstrated on testing example of hydrogen atom.
We are able to obtain some results which are impossible in the framework of
standard Maxwell electrodynamics. The Sommerfeld - Dirac formula for the fine
structure of the hydrogen atom spectrum is obtained on the basis of such
Maxwell equations without appealing to the Dirac equation. The Bohr postulates
and the Lamb shift are proved to be the consequences of the equations under
consideration. The relationship of the new model with the Dirac theory is
investigated. Possible directions of unification of such electrodynamics with
gravity are mentioned.
