  Schr\"odinger equation for pair of two massless Dirac particles when magnetic
field is applied in Landau gauge is solved exactly. In this case the separation
of center of mass and relative motion is obtained. Landau quantization
$\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a
Coulomb potential from massless chiral Dirac equation in cylindric coordinate
is found. The root ambiguity in energy spectrum leads into Landau quantization
for bielectron, when the states in which the one simultaneously exists are
allowed. The tachyon solution with imaginary energy in Cooper problem
($\epsilon^{2}<0$) is found. The continuum symmetry of Dirac equation allows
perfect pairing between electron Fermi spheres when magnetic field is applied
in Landau gauge creating a Cooper pair.
