This paper presents an original investigation of the motion at the band crossing points in the energy
dispersion of either bulk crystals or inversion layers. In particular, by using a formalism based on
the time dependent Schrödinger equation, we address the quite elusive topic of the belonging of the
carriers to the bands that are degenerate at the crossing point. This problem is relevant and delicate
for the semiclassical transport modeling in numerically calculated band structures; however, its
clarification demands a full-quantum transport treatment. We here propose analytical derivations and
numerical calculations clearly demonstrating that, in a given band structure, the motion of the
carriers at the band crossing points is entirely governed by the overlap integrals between the
eigenfunctions of the Hamiltonian that has produced the same band structure. Our formulation of the
problem is quite general and we apply it to the silicon conduction band calculated by means of the
nonlocal pseudopotential method, to the hole inversion layers described by a quantized k·p
approach, and to the electron inversion layers described by the effective mass approximation
method. In all the physical systems, our results underline the crucial role played by the
abovementioned overlap integrals.
