The diffraction and spreading of a wavepacket, Guy Vandergrift, Am. J. Phys. 72(3)
The spreading of a one-dimensional wavepacket solution of Schrödinger's equation is related to the diffraction of light, as can be verified by considering the spreading of a wavepacket for an arbitrary dispersion relation. This investigation uncovers a special symmetry will preserve this symmetry in all Galilean reference frames. This property leads to a derivation of deBroglies's postulate that wave number is proportional to momentum (or velocity). The application to non-Gaussian wavepackets and to Fraunhoffer diffraction also is discussed.