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<font face="serif">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. <br>
<br>
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 <i>Introducti</i><i>on
to Quantum </i><i>Mechanics, </i>the "Bible" of calculations
for old style method using these function (Morse and Feschbach, <i>Methods
of Theoretical Physics) </i>a more modern day version of Morse
and Feschbach (Arfken, <i>Mathematical Methods for Physic</i><i>ists</i>)
and another standard text for computing (Abramowitz and Stegun, <i>Handbook
of Mathematical Functi</i><i>ons</i>) ALL DISAGREE ON THE
NORMALIZATION CONSTANT.<br>
<br>
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.<br>
<br>
<br>
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<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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