Anomalous transparency for near-top Bloch states of periodic potential

In the paper are considered stationary (Bloch) states of a particle, in the field of periodic biparabolic type potential. It is shown that while the particles energy decreases in limits of a single energy band, the probability of the particle to be in barrier-type region of periodic potential increases, in contrary to the expected decreasing. This anomalous behavior is more pronounced for the near-top bands and monotonically decreases for the higher or lower ones.