  We show that a noncyclic phase of geometric origin has to be included in the
approximate adiabatic wave function. The adiabatic noncyclic geometric phase
for systems exhibiting a conical intersection as well as for an Aharonov-Bohm
situation is worked out in detail. A spin-1/2 experiment to measure the
adiabatic noncyclic geometric phase is discussed. We also analyze some
misconceptions in the literature and textbooks concerning noncyclic geometric
phases.
