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Momentum of constant wave function
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[QUOTE="J.L.A.N., post: 5251192, member: 441612"] [B]1. The scenario[/B] 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? [h2]Homework Equations[/h2] I. Âψ = Aψ (A being the measured eigenvalue corresponding to the Hermitian operator Â) II. [B]p[/B] = -iħ[B]∇[/B] III. ψ[SUB]x=0[/SUB] = ψ[SUB]x=L[/SUB] (Periodic b.c. for each of the three pairs of opposite sides of the larger cuboid) IV. [x[SUB]i[/SUB],p[SUB]j[/SUB]] = iħδ[SUB]i,j[/SUB] [B]3. The attempt[/B] 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 [I]constant[/I] 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? [/QUOTE]
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Momentum of constant wave function
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