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Gaussian Wavepackets

  1. Oct 9, 2008 #1
    I'm starting a project on Gaussian Wavepackets, and the evolution of the Uncertainty principle with time, however after the summer I'm a bit rusty :s, so I have a few questions, if anyone could help that would be great.

    Ok, first of all I see (and largely understand) that delta-x delta-p > h-bar/2, but I would like to know how delta-x = RMS(x)? It's probably basic but I need good foundations....

    Also, what is the general equation for a gaussian wavepacket?

    Any help would be great, thanks!
     
  2. jcsd
  3. Oct 9, 2008 #2
    delta-x = RMS(x) is the definition of delta-x. What else is there to understand? Theres no physical meaning to the relation, its just what delta-x is defined as.

    as for the general equation of the gaussian wavepacket, I believe it is just the free particle wave function multiplied by a gaussian function.
     
  4. Oct 9, 2008 #3

    jtbell

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    Staff: Mentor

    Try a Google search for Gaussian wave packet. :smile:
     
  5. Oct 9, 2008 #4
    Yea I was going to say that, except I actually tried doing that search and I just could not find a general equation for the gaussian wave packet.
     
  6. Oct 9, 2008 #5

    jtbell

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    Staff: Mentor

    The very first hit that I see has a rather detailed discussion of Gaussian wave packets, including the derivation of an explicit form of the initial wave function for one.

    A full, explicit, time-dependent wave function that contains the spreading is another matter. I know it's in at least one textbook, Morrison's "Understanding Quantum Physics." The link above doesn't have that, but it does have an equation for the width of the packet as a function of time.
     
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