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3. (a) Show that for a freely moving matter particle (in a zero potential energy region)...

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3. (a) Show that for a freely moving matter particle (in a zero potential energy region) that the wave function: Ψ(x, t) ei(k

3. (a) Show that for a freely moving matter particle (in a zero potential energy region) that the wave function: Ψ(x, t) ei(kx-at) is a solution to the time-dependent Schrödinger equation if the angular frequency o(k) is a function of the wavenumber k, given by hk2 o(k) = (b) Show that the group velocity vg for a packet of waves having o(k) from part (a) is equal to the particle velocity v from the non-relativistic momentum relation p = mv. (c) Show that the phase velocity of a constituent wave is approximately equal to one half of the group velocity.

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