In the framework of the theory of an electron in a periodic potential, we
reconsider the longstanding problem of the existence of smooth and periodic
quasi-Bloch functions, which is shown to be equivalent to the triviality of the
Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and
some bundle-theoretic methods, we show that the problem has a positive answer
for any d < ... [Show full abstract] 4, thus generalizing a previous result by G. Nenciu. We provide a
general formulation of the result, aiming at the application to the Dirac
equation with a periodic potential and to piezoelectricity.