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Posted by Alexander on July 10, 2001 21:53:18 UTC

If you have a wave packet of 10 wavelength long, its wave number k (which is Fourie - image of its length) is 1/10 wide. Thus its momentum p is 10% uncertain. If a wave packet is 1000 waves long, Fourie transform of that is 1/1000 wide (uncertain), thus momentum is 0.1% uncertain. The product of (length of wave bunch x wave number uncertainty) is always 1 (by the definition of a wave number as a Fourie transform of a packet length). The length of a wave packet is what we call uncertainty of position of wave (indeed, Q: where is the wave bunch with the length equal to 1 meter is located? A: somewhere within this 1 meter). The width of wave number distribution is what we call uncertainty of wave number k. Multiply the equation (delta x)(delta k)=1 by Plank constant h, and you get fundamental to quantum mechanics Heizenberg uncertainty principle: (delta x)(delta p)=h.

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