Institute of Physics, NAS of Belarus,

For the Euclidean 3-space, there is known 12 systems of orthogonal coordinates allowing for the complete separation of the variables in the covariant Laplace equation, the last is closely related to Schrodinger equation. This problem becomes much more involved when turning, for instance, to the Dirac or Maxwell equations; and it still remains unsolved in full.However, it is known that with the use of squaring procedure for the Dirac equation leading to the scalar Klein -- Fock -- Gordon equation, one may construct solutions in separated form of the Dirac equation as well, using such solutions for the scalar equation. Therefore, the possibility to get solutions for the Klein-Fock-Gordon equation in all 12 coordinate systems, permits us to expect existence of similar solutions for the Dirac equations as well. Similar possibility exists also for the Maxwell theory. In the present article, we will examine the possibility to separate the variables for Maxwell equations. This task is solved with the use of the matrix Majorana-Oppenheimer approach to Maxwell theory. Within this formalism, the problem reduces to studying the system of four 1st order equations for three complex - valued function, $\vec{f} = \vec{E} +i \vec{B}$.