Geometric phases and exactly solvable time-dependent potentials

A method of constructing periodic time-dependent Hamiltonians admitting exact solutions is used to study the geometric phase. The approach is based on the transformation of soluble time-independent equations into time-dependent ones by employing a set of special time-dependent transformation operators. A class of periodic time-dependent Hamiltonians with cyclic solutions is constructed in a closed analytic form and the nonadiabatic geometric phase is determined in terms of the obtained solutions.