- #36
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Great paper. I'll have a close look at it. I must say, I can understand now, why the diffraction is not treated in standard textbooks. I couldn't solve the appropriate Helmholtz equation with the exact boundary conditions exactly, even not for a circular apperture. The best, I can come up with is the standard Sommerfeld-corrected approximate Kirchhoff solution, which should be a good approximation in the limit, where the de Broglie wavelength is small compared to the dimensions of the apperture, using the Green's function for the infinite plane. At the moment I'm at the process to get some numerical calculations done :-).
Of course the free-particle wave packet can be described pretty well in a classical approximation. Since there's no force, the leading-order classical approximations give the classical uniform motion: Ehrenfest's theorem together with the fact that the equations of motion in the Heisenberg picture are linear in position and momentum operators and are of the classical form; taking the averages gives then the classical equation of motion also for the expectation values.
Of course the free-particle wave packet can be described pretty well in a classical approximation. Since there's no force, the leading-order classical approximations give the classical uniform motion: Ehrenfest's theorem together with the fact that the equations of motion in the Heisenberg picture are linear in position and momentum operators and are of the classical form; taking the averages gives then the classical equation of motion also for the expectation values.