Phase coherence and ``fragmented'' Bose condensates

We show that a ``fragmented Bose condensate'' in which two or more distinct single-particle states are macroscopically occupied by the same species of boson is inherently unstable to the formation of a conventional Bose condensate whose macroscopically occupied state is a linear combination of the ``fragments'' with definite relative phases. A related analysis shows that a reproducible relative phase develops when two initially decoupled condensates are placed in contact.