Harmonic Oscillators and FTs

So I was thinking about how holes originate from an assumption of quadradically dependent dispersion relations. This is essentially the same as assuming a simple harmonic oscillator.

 I recall a article/forum post* that said all applied physics is simple harmonic oscillators and Fourier transforms. This is almost true for our case. We use Fourier transforms to move to reciproical space and this is the basis of the majority of our analysis. The Bloch model extends this even further as even energy band gaps are just the Fourier components!

 A simple harmonic oscillator allows us to understand holes, a very physically meaningful and intuitive quasi particle. In my earlier encounters with holes I just believed them to be real because they make sense.

 Its interesting that a couple of mathematical tools can bring so much physical insight into vastly different applications. Perhaps I should have paid more attention to Fourier transforms in previous years ;) Good thing simple harmonic oscillators are simple. Even in quantum mechanics they are really nice :)

I propose a new judge on the beauty of a theory. The simpler a simple harmonic oscillator is in this theory the more elegant the theory. That's why quantum is much more elegant than classical mechanics! But I digress...

 Can anyone else think of examples from this course of simple harmonic oscillator power??

 Andy PS Hugh David Politzer 2004 Noble Prize Laureate sung a song about the simple harmonic oscillator.

 *Citation Needed