Thursday, September 4, 2014

Classic Element of Theoretical Work

Dear Diary,

Dave, my new office mate, is busy doing something.  He had an issue finding the number of particles from a density, so he asked me what could possibly be wrong.

I immediately leapt to the error that I always (and still sometimes do) make:  we work in one dimension, so integrating the density requires just integrating the density.  Then, all of a sudden, maybe Kieron asks a 3D question in the ABCs and you forget to put in the Jacobian (4*Pi*r^2).  But once you realize that, everything is solved!*

He then promised to take me to dinner, but I'm not sure if I earned it just yet...and now he's excited dancing--sort of mosh pit style.  You go, Dave.

*-Oh no...here comes a harder question about Thomas-Fermi theory and Lieb-Oxford bounds...

1 comment:

1. The Jacobian for the cartesian-spherical coordinates transformation is r^2 \sin \theta. Only if the integrand is spherically symmetric and only after integration over the complete domain of the solid angle one obtains 4\pi r^2.