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The Uncertainty Principle
If the entire universe consists of waves when viewed on the smallest scales, what is a
particle? A particle is a
wave packet
. Consider the graph shown below where two sine
waves of slightly different frequency are superposed, creating a periodic variation in
amplitude. What is most remarkable about this simple combination is that, if the waves
are set in motion, frequencies and wavelengths can be selected that will make the bulges
move at a different speed than the advancing waves that compose them. They can even
go in opposite directions.
If a larger number of sine waves are superposed, it is even possible to select a set of
parameters such that the combination has a significant amplitude at essentially one
location only. The form below was created by taking the sum of the first ten cosine waves
of the form
y =
cos
(Nx)
where
N
is a positive integer. If more waves were summed, the
isolation of the pulse at the center would become more and more perfect. If the wave
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This note was uploaded on 04/05/2012 for the course PHYS 131 taught by Professor Tibbets during the Spring '11 term at Cuyamaca College.
 Spring '11
 Tibbets
 Heisenberg Uncertainty Principle, Light

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