  Carl Bender and collaborators have developed a quantum theory governed by
Hamiltonians that are PT-symmetric rather than Hermitian. To implement this
theory, the inner product was redefined to guarantee positive norms of
eigenstates of the Hamiltonian. In the general case, which includes arbitrary
time-dependence in the Hamiltonian, a modification of the Schrodinger equation
is necessary as shown by Gong and Wang to conserve probability. In this paper,
we derive the following selection rule: transitions induced by time dependence
in a PT-symmetric Hamiltonian cannot occur between normalized states of
differing PT-norm. We show three examples of this selection rule in action: two
matrix models and one in the continuum.
