[CHM 331] That was a mess...

[Andrew J. Pounds]

So Kaydren noted a problem with the hydrogenic wavefunction Mathematica 
file I sent you about a week ago.   It gave incorrect answers for the 2s 
orbital when compared with your book.    Unfortunately I sent you all a 
file that was "in progress" and not the right one.   I was playing 
around this past summer with this in hopes of using it a as a part of 
CHM 372; I apparently never finished it.

The issue with the one I sent you had to do with the normalization 
constant for the associated Laguerre polynomials.  Rather than just 
playing with Mathematica, I decided to head back to my office and see if 
I could get some guidance on how to set this up properly.   This became 
an interesting problem as a fundamental texts in quantum mechanics 
(Eyring, Walters, and Kimball /Introducti//on to Quantum //Mechanics, 
/the "Bible" of calculations for old style method using these function 
(Morse and Feschbach, /Methods of Theoretical Physics) /a more modern 
day version of Morse and Feschbach (Arfken, /Mathematical Methods for 
Physic//ists/) and another standard text for computing (Abramowitz and 
Stegun, /Handbook of Mathematical Functi//ons/) ALL  DISAGREE ON THE 
NORMALIZATION CONSTANT.

I sat down and derived a normalization constant that should work with 
the associated Laguerre function that is in found in Mathematica and 
that works for the hydrogen atom to produce expectation values with 
respect to the  Bohr radius.   I know that it works for the S orbitals 
but have not tested it fully for the P, D, and F orbitals.  The modified 
Mathematica notebook is attached.  Let me know if you have any problems 
opening or using it.


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

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