[CHM 330] Project 3

[Andrew J. Pounds]

Good morning class.  I have gotten several questions in the last 24 
hours about what bounds to use when searching for the eigenvalues of the 
finite well potential.  That will vary from person to person, but the 
intent of the "plot" option was to help you find those.   I encourage 
you to use the sample potential data that I provided in the project 
description as well as my example results to help you verify that you 
are doing things correctly.  With that in mind, here is the plot for the 
even function using the potential well data provided in the description 
(yours will be different).

plot

The three vertical lines represent places that the function is 
discontinuous.  You function should have zeros between 0 and the first 
vertical line around 0.035, another zero between 0.05 and 0.3, and 
another zero between 0.4 and 0.9.  There could also be a root in that 
last interval between 0.95 and 1 depending on how deep and wide the well 
is.  Anyway, you would use those three different sets of bounds to find 
the roots - which will be the alpha values.  . If you look at the 
project description, those even roots occur at 0.0298, 0.02655, and 
0.07153.  There should be exactly one root in each region between the 
discontinuities (except for the last region on the right where they may  
or may not be a root).

Please note - if you try search over a discontinuity with your bounds 
you may actually find a false (and incorrect) root that is a result of 
the incapability of the algorithm to function over a discontinuity.  
Stay away from the discontinuities.

You may have to experiment some and play around with the bounds to get 
the right values, but I can promise you that all of the models I sent 
out work and will give at least one (and probably many more) even and 
odd solutions.

Keep the questions coming.  I have been answering many questions about 
the project daily for the past week and a half - including numerous ones 
while I was on the road with my family.  Sunday afternoon, starting 
around 5 pm -- I will be unable to answer questions for the rest of the 
day.  If you need your project data or need to have anything answered 
before the project is due, you have between now and then to ask it.


-- 
*/Andrew J. Pounds, Ph.D./*
/Professor of Chemistry and Computer Science/
/Director of the Computational Science Program/
/Mercer University/
/1501 Mercer University Drive, Macon, GA 31207 /
/(478) 301-5627/
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