  We discuss the calculation of semi-classical wormhole vertex operators from
wave functions which satisfy the Wheeler-deWitt equation and momentum
constraints, together with certain `wormhole boundary conditions'. We consider
a massless minimally coupled scalar field, initially in the spherically
symmetric `mini-superspace' approximation, and then in the `midi-superspace'
approximation, where non-spherically symmetric perturbations are linearized
about a spherically symmetric mini-superspace background. Our approach suggests
that there are higher derivative corrections to the vertex operator from the
non-spherically symmetric perturbations. This is compared directly with the
approach based on complete wormhole solutions to the equations of motion where
it has been claimed that the semi-classical vertex operator is exactly given by
the lowest order term, to all orders in the size of the wormhole throat. Our
results are also compared with the conformally coupled case.
