We present a pedagogical discussion on the time evolution of a Gaussian neutrino wave packet in free space. A common treatment is to keep momentum terms up to the quadratic order in the expansion of the energy-momentum relation so that the Fourier transform can be evaluated analytically via Gaussian integrals. This leads to a solution representing a flat Gaussian distribution with a constant longitudinal width and a spreading transverse width, which suggests that special relativity would be violated if the neutrino wave packet were detected on its edge. However, we demonstrate that by including terms of higher order in momentum the correct geometry of the wave packet is restored. The corrected solution has a spherical wave front so that it complies with special relativity.
|Original language||English (US)|
|Number of pages||5|
|State||Published - 2015|
|Event||13th International Conference on Topics in Astroparticle and Underground Physics, TAUP 2013 - , United States|
Duration: Sep 8 2013 → Sep 13 2013
Bibliographical noteFunding Information:
This work was supported in part by the US DOE Award No. DE-FG02-87ER40328.
- neutrino wave packet
- quantum mechanics
- special relativity