If quantum mechanics requires the singlevaluedness of the wave function as a solution to the Schroedinger equation, how can it possibly explain the multivaluedness of the phase in the ESAB effect? How can the phase be described by a solid angle of a geodesic triangle on the Poincaré sphere, as in Berry's analogy with the Pancharatnam phase due to the interference of polarized light in different states, when all the relevant information lies on the surface of the Poincaré sphere?