A Note Concerning von Neumann Projector Measurement Pointer States, Weak Values, and Interference

It is well known that the pointer state |{\Phi}> resulting from the von Neumann measurement of a projection operator A performed upon an ensemble of quantum systems in the preselected state |{\psi}> depends upon A|{\psi}>. Here it is shown that the pointer state |{\Psi}> obtained from such a measurement performed upon an ensemble that is also postselected depends upon the weak value of A - regardless of the measurement interaction strength. It is also found that, while the spatial distribution of |{\Psi}> exhibits interference, the idempotency of A prohibits interference in that of |{\Phi}>. This is explained in terms of welcher Weg information.