## A Mathematical Addendum

Quantum Mechanics and Momentum
Part 3′ (Mathematical Addendum): Fourier Transforms and Derivatives.

Again, we have our Fourier transform . Now, let us consider the transform of the derivative of a function, . We can use integration by parts on this: with , ; we have , and , and so
.

Now, if we require  (as any meaningful signal, or quantum wavefunction, must be), the first term on the right side of the above vanishes, and thus:
.

This will prove important in later posts.

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### 2 Responses to “A Mathematical Addendum”

1. Physics Friday 47 « Twisted One 151’s Weblog Says:

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2. Monday Math 128 « Twisted One 151's Weblog Says:

[…] Math 128 By twistedone151 We have previously discussed the Fourier transform (here and here, especially). In this post, we noted that (using the symmetric angular convention) the space […]