  We present a method for calculating the Aharonov-Anandan phase for
time-independent Hamiltonians that avoids the calculation of evolution
operators. We compare the generic method used to calculate the Aharonov-Anandan
phase with the method proposed here through four examples; a spin-1/2 particle
in a constant magnetic field, an arbitrary infinite-sized Hamiltonian with two
known eigenvalues, a Fabry-Perot cavity with one movable mirror and a three
mirrors cavity with a slightly transmissive movable middle mirror.
