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 three-dimensional spreading of a wavepacket for an arbitrary dispersion relation. This investigation uncovers a special property of Schrödinger’s equation for a free particle: A wavepacket with initial spherical symmetry will preserve this symmetry in all Galilean reference frames. This property leads to a derivation of de Broglie’s postulate that wave number is proportional to momentum (or velocity). The application to non-Gaussian wavepackets and to Fraunhoffer diffraction also is discussed.
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NOTES AND DISCUSSIONS| March 01 2004
The diffraction and spreading of a wavepacket
Guy Vandegrift; The diffraction and spreading of a wavepacket. Am. J. Phys. 1 March 2004; 72 (3): 404–407. https://doi.org/10.1119/1.1591763
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