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In QM particles have wavefunctions that disperse quite fast. The FWHM for gaussian wavepacket increases in time as $\Delta x(t)= \Delta x_0\sqrt{1+(t/\tau)^2} $, $\tau=2m(\Delta x_0)^2/\hbar$

  1. What happens with the particle after 1 second? $\Delta x_0=1pm$, $\Delta x(1s)=6\cdot10^7m$ using the electron mass.

  2. Does it mean that the uncertainty where it is increases but the particle has same radius wherever it is?

  3. How this particle will behave in Bohmian mechanics?

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closed as unclear what you're asking by ACuriousMind, CuriousOne, Diracology, user36790, knzhou Jul 25 '16 at 7:08

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  • $\begingroup$ It's all a question of the momentum. High energy aka high momentum states don't disperse "fast". They can form tracks that are many orders of magnitude longer than the de Broglie wavelength of the quanta, i.e. the spatial scales that matter are energy and momentum dependent, rather than absolutes. You need to be careful with assigning radii to quanta. Quanta are not objects but properties of fields and whatever radius we quote for composite particles or as semi-classical charge radii is only meaningful in certain (usually low energy) contexts. $\endgroup$ – CuriousOne Jul 25 '16 at 0:01
  • $\begingroup$ Thanks would that mean that 1eV electron disperses differently than 10keV electron ? $\endgroup$ – Anonymous Jul 25 '16 at 0:16
  • $\begingroup$ It depends on the observer. An observer "in the rest system of the quantum" will see the Gaussian state, but an observer moving at nearly the speed of light relative to it will see a high energy "particle" that leaves a track in detectors. What we see of the world depends on who we are, in quantum mechanics much more so than in classical mechanics (but even there it matters). $\endgroup$ – CuriousOne Jul 25 '16 at 0:34
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The radius of the wavepacket is unrelated to the radius of the particle. For instance you could have a particle of zero size (as the electron is suspected) but whose probability of being found somewhere has a certain size. For instance a wave packet: The wave packet only gives you the probability of finding a particle at that place (that is, more likely inside the wave packet), but the wave packet does not correspond to the size of the particle. It is not the case that the particle is spread in the same way as the location probability distribution.

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