  We have proposed a fully quantum approach to non-perturbatively calculate the
spin-split Landau levels and g-factor of various spin-orbit coupled solids,
based on the k.p theory in the matrix mechanics representation. The new method
considers the detailed band structure and the multiband effect of spin-orbit
coupling irrespective of the magnetic field strength. An application of this
method to PbTe, a typical Dirac electron system, is shown. Contrary to popular
belief, it is shown that the spin-splitting parameter M, which is the ratio of
the Zeeman to cyclotron energy, exhibits a remarkable
magnetic-field-dependence. This field-dependence can rectify the existing
discrepancy between experimental and theoretical results. We have also shown
that M evaluated from the fan diagram plot is different from that determined as
the ratio of the Zeeman to cyclotron energy, which also overturns common
belief.
