First, write out .
We expect to need to keep the radial derivatives so lets identify those by dotting into . This will also make the units match .
By adding these two expressions, things simplify a lot.
We can now solve for and we have something we can use in the Schrödinger equation.
The Schrödinger equation now can be written with only radial derivatives and
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Jim Branson 2013-04-22