  We extend to quantum mechanical systems results previously obtained for
classical mechanical systems, concerning time reversibility in presence of a
magnetic field. As in the classical case, results like the Onsager reciprocal
relations are consequently obtained, without recourse to the Casimir
modification. The quantum systems treated here are nonrelativistic, and are
described by the Schr{\"o}dinger equation or the Pauli equation. In particular,
we prove that the spin-field interaction does not break the time reversal
invariance (TRI) of the dynamics, and that it does not require additional
conditions for such a symmetry to hold, compared to the spinless cases.
