  In the Jaynes-Cummings model a two-level atom interacts with a single-mode
electromagnetic field. Quantum mechanics predicts collapses and revivals in the
probability that a measurement will show the atom to be excited at various
times after the initial preparation of the atom and field. In retrodictive
quantum mechanics we seek the probability that the atom was prepared in a
particular state given the initial state of the field and the outcome of a
later measurement on the atom. Although this is not simply the time reverse of
the usual predictive problem, we demonstrate in this paper that retrodictive
collapses and revivals also exist. We highlight the differences between
predictive and retrodictive evolutions and describe an interesting situation
where the prepared state is essentially unretrodictable.
