# Momentum of constant wave function

J.L.A.N.
1. The scenario
If we have a small cuboid volume embedded in a larger dito with periodic boundary conditions, and a wave function that is constant inside the former, while zero everywhere else; what can we then know about the momentum?

## Homework Equations

I. Âψ = Aψ (A being the measured eigenvalue corresponding to the Hermitian operator Â)
II. p = -iħ
III. ψx=0 = ψx=L (Periodic b.c. for each of the three pairs of opposite sides of the larger cuboid)
IV. [xi,pj] = iħδi,j

3. The attempt
I'm thinking about the standard approach (I.) of measurement by acting on the wave function with the Hermitian operator corresponding to the quantity of interest - in this case the momentum, the operator of which is written just above (II.). Acting on a constant wave function the result is obviously zero (since we are differentiating a constant function), but I am not sure of what this really tells us about the momentum in general, for the above scenario. Is there any other approach that could produce a non-zero momentum (perhaps by utilizing (III.))? What about the discontinuity at the boundary of the inner volume?