BLOCH THEOREM FOR THE EVOLUTION OF STATES IN A CYCLIC QUANTUM SYSTEM AND A NEW-TYPE OF QUANTUM PHASES

It is found that in a quantum system with cyclic Hamiltonian the time- dependent Schrodinger equation admits the Bloch type solutions which h ave the form of Bloch function with respect to the time. These solutio ns constitute an orthonormal basis of the solution space and lead to a new type of quantum phases. The new phases, called Bloch phases by th e authors, are the special Aharonov-Anandan phases, and reduce to the Berry phases under the adiabatic approximation if the degeneracy of in stantaneous eigenenergy is time-independent. The above conclusions are proved and calculation for the evolution of spin magnetic moments in a magnetic field precessing with constant angular velocity is exemplif ied.