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<p>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).</p>
<p><img moz-do-not-send="false"
src="cid:part1.uZ2wtOHu.ifW83pF6@sandbox.mercer.edu" alt="plot"
width="640" height="480"></p>
<p>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).</p>
<p>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. <br>
</p>
<p>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.</p>
<p>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. <br>
</p>
<br>
<div class="moz-signature">-- <br>
<b><em>Andrew J. Pounds, Ph.D.</em></b><br>
<em>Professor of Chemistry and Computer Science</em><br>
<em>Director of the Computational Science Program</em><br>
<em>Mercer University</em><br>
<em>1501 Mercer University Drive, Macon, GA 31207 </em><br>
<em>(478) 301-5627</em><br>
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