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Propagation of wave packet

  1. Oct 19, 2009 #1
    The idea of a wave packet is confusing a bit. First let me tell you what I have understood about it. A wave packet is obtained by the superposition of harmonic waves of nearby frequencies which represents a matter wave. It is well known fact that the width of a moving Gaussian wave packet in free space is time dependent due to uncertainty in momentum which leads to uncertainty in velocity. If the wave packet represented a microscopic particle its width will increase rapidly due Heisenberg’s uncertainty principle. If the same wave packet is moving in a dispersive medium, the spreading is further enhanced due to wavelength dependence of phase velocity. Is it right? Assume that time tends to infinity.
     
  2. jcsd
  3. Oct 19, 2009 #2
    In the classical mechanics any uncertainty in the initial velocity v0 leads to a spreading uncertainty in the final position too: ∆x(t) = ∆v0*t = ∆p*t/m.
     
    Last edited: Oct 19, 2009
  4. Oct 19, 2009 #3
    Yes.

    Not necessarily. Heisenberg's uncertainty principle relates the spatial spread of the packet with the range of frequencies in it. Unlike a point particle, a properly constructed wave packet may be quite stable.

    Again, not necessarily - dispersion can act to inhibit rather than enhance the spread.
     
  5. Oct 22, 2009 #4
    Thanx guys for sharing your knowledge with me.
     
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