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!