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mathman

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chroot

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The "delta function" is not really a rigorously defined mathematical function, but nonetheless us physicists often use it as if it were.Originally posted by theFuture

Can you think of any other physical examples?

The delta is one of those weird things like pi that just manages to show up in solutions all the time. You'll find deltas all over physics, particularly quantum mechanics.

To give a simple physical example, take a pure sine wave of one frequency -- say middle A, 440 Hz. If you plot the frequency (spectral) content of this signal, you'll see a delta function -- exactly one frequency is present, and all the signal's power is in it.

This same sort of thing happens in quantum mechanics -- if you have a particle with a precisely known momentum, its momentum is a delta function in momentum-space.

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Suffice it to say, the delta function is a subtle creature and is difficult to understand.

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