Gaussian wavepacket

  • Thread starter solas99
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how can the gaussian wavepacket presents a physical picture of the origin of position-momentum uncertainty?
 

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jtbell
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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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