Quantum Phases of Pancharatnam Type for a General Spin in a Time-Dependent Magnetic Field

Based on the quantum invariant theory, the quantum phases, including the total phase as well as its dynamical and geometric parts, of Pancharatnam type are derived for a general spin in a time-dependent magnetic field, without the constraint of adiabatic, cyclic or unitary condition. The geometric meaning of geometric phase is expounded.