Wednesday, October 22, 2014

Not Obvious

Dear Diary,

For months now, I've been hoping to figure out what exactly Lucas did to derive the exchange functional.  Well, as fate would have it, I just did.

The trick involved taking a double integral in one dimension and noting that the integrand only contained the difference of the two coordinates.  The replacement is obvious if you wave your hands!  I get the feeling that this is a common trick in the ABCs but it must've flown completely over my head!  Li recognized the switch as from a particular class of problems (the Hooke's atom) but man...the math step was not obvious!

In my defense, I did ask Lucas several times for how he did this and nowhere in the notes was this trick.  I kept getting an exponential integral.  Playing Devil's advocate, however, I should have learned it during the now fifth ABC class I'm in!  Again in my defense, somehow this should have been exposed, you'd think.  Again playing Devil's advocate:  go and do your work!  Stop blogging!

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