  The physical condition that the expectation values of physical observables
are real quantities is used to give a precise formulation of PT-symmetric
quantum mechanics. A mathematically rigorous proof is given to establish the
physical equivalence of PT-symmetric and conventional quantum mechanics. The
results reported in this paper apply to arbitrary PT-symmetric Hamiltonians
with a real and discrete spectrum. They hold regardless of whether the boundary
conditions defining the spectrum of the Hamiltonian are given on the real line
or a complex contour.
