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.


Tags: , , ,

2 Responses to “A Mathematical Addendum”

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

    […] One 151’s Weblog Just another WordPress.com weblog « A Mathematical Addendum Monday Math 47 […]

  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 […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: