  In the paper complete systems of exact solutions for Dirac and Weyl equations
in the Lobachevsky space are constructed on the base of the method of
separation of the variables in quasi-cartesian coordinates. An extended
helicity operator is introduced. It is shown that solution constructed when
translating to the limit of vanishing curvature coincide with common plane wave
solutions on Minkowski space going in opposite z-directions. It is shown the
problem posed in Lobachevsky space simulates a situation in the flat space for
a quantum-mechanical particle of spin 1/2 in a 2-dimensional potential barrier
smoothly rising to infinity on the right.
