Geometric phases, symmetries of dynamical invariants and exact solution of the Schrödinger equation (Q2766165)

The author considers the Aharonov-Anandan nonadiabatic generalization of Berry's phase of a quantum system. This generalization is called the geometric phase. The notion of geometrically equivalent quantum systems is introduced with the meaning that such systems have the same geometric phase. The class of geometrically equivalent quantum systems is characterized in the paper by their common invariant and it is shown that their Hamiltonians and evolution operators are related by symmetry transformations of the invariant. Some applications (to periodic case, to cranked Hamiltonians, etc.) are described.