I haven’t given up learning QM yet. I almost did give up. Ha not really! I’ve done the math behind QM in school so why would I quit?

Okay, Mr susskind in his Modern Physics lecture ( http://youtu.be/LBFBQr_xKEM?t=34m54s ) does something really cute using Dirac notation, like:

<x|k> = e^(ikx)/sqrt(2pi) is the projection (inner product) of a vector k (momentum) onto a position basis.

Then he does something like

Psi^hat( k ) = <k|Psi>

= integral { <k|x> <x | Psi> } dx }

= 1/sqrt(2pi) integral { e^(-ikx) Psi(x) } dx }

It’s called a fourier transform!

If you done any graphics you may have used Spherical Harmonics for lighting ( where you reconstruct a lighting function by projecting the coefficients of a lighting function). It’s the same idea. Spherical Harmonics are the solutions to the Laplacian equation (http://en.wikipedia.org/wiki/Laplace’s_equation).