  The general solution of the Dirac equation for quasi-two-dimensional
electrons confined in an asymmetric quantum well, is found. The energy spectrum
of such a system is exactly calculated using special unitary transformation and
shown to depend on the electron spin polarization. The general solution, being
the only one, contains free parameters, whose variation continuously transforms
one known particular solution into another. As an example, two different cases
are considered in detailL: electron in a deep and in a strongly asymmetric
shallow quantum well. The effective mass renormalized by relativistic
corrections and Bychkov-Rashba coefficients are analytically obtained for both
cases. The general solution allows - independently on the existence of the spin
invariants - to establish conditions at which a specific (accompanied or
non-accompanied by Rashba splitting) spin state can be realized. In principle,
this opens new possibilities of the spin degree of freedom control in
spintronics via synthesis of heteroctructures of the desirable properties.
