Quantum-mechanical stationary states are of the general form Ψ(x,t)=ψ(x)e-iωt. For the basic plane wave (Chapter 4), this is Ψ (x,t)=A elkx e-iωt=Aei(kx-ωt) and for a particle in a box, it is Ψ(x, t)=A sin(kx) e-iωt. Although both are sinusoidal, we claim that the plane wave alone is the prototype function whose momentum is pure—a well-defined value in one direction. Reinforcing the claim is the fact that the plane wave alone lacks features that we expect to see only when, effectively, waves are moving in both directions. What features are these, and, considering the probability densities, are they indeed present for a particle in a box and absent for a plane wave?
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