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Gaussian wavepacket

  1. Jan 14, 2012 #1
    how can the gaussian wavepacket presents a physical picture of the origin of position-momentum uncertainty?
     
  2. jcsd
  3. Jan 14, 2012 #2

    jtbell

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    Staff: Mentor

    I would prefer to say that the Gaussian wave packet is an example of position-momentum uncertainty.

    All wave packets, no matter what shape, have a position-momentum uncertainty relationship ΔxΔp = k, where k depends on the shape of the packet. The Gaussian wave packet is special because it can be shown from Fourier analysis theory that it has the smallest k, namely [itex]\hbar / 2[/itex]. All other shapes of packets have larger k's. Therefore for any wave packet,

    [tex]\Delta x \Delta p \ge \frac{\hbar}{2}[/tex]

    (the Heisenberg uncertainty principle)
     
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