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<div class="moz-cite-prefix">On 02/07/2017 08:09 PM,wrote:<br>
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cite="mid:a33cdc171c7a4610b15545068e478f3e@spiderman.MercerU.local"
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<p>Dr. Pounds,</p>
<p><br>
</p>
<p>On Part B of the Chapter 15 Particle in a Box problem that
deals with P(x) how am I to determine the integral parameters?
Like for E1 I want to use 0.5/a but I don't get any of the
answer choices when I do it that way. And when I use a/0.5
then I can't cross out the a's in sin(2pix/a). Does "a" have a
value that I'm just not getting? So far I have </p>
<p style="text-align: center; ">2/a[x-(a/2pi)sin(2pix/a)]</p>
<p style="text-align: left;">It's just the integral parameters
that I don't get. </p>
<p style="text-align: left;"><br>
</p>
<p style="text-align: left;">Thanks,</p>
<p style="text-align: left;"><br>
</p>
<p style="text-align: left;"><br>
</p>
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<p><font face="serif">So I am assuming that you are talking about
problem 15.34. On part B all space would be on the open
interval <img style="vertical-align: middle"
src="cid:part1.31AE893B.00D0927A@mercer.edu"
alt="$(-\infty,\infty)$">, but we know that for this box,
since it has a length of <img style="vertical-align: middle"
src="cid:part2.787728CA.3D420860@mercer.edu" alt="$l$">, that
"all space" will be on the closed interval <img
style="vertical-align: middle"
src="cid:part3.78C5790B.51BD08B4@mercer.edu" alt="$[0,a]$">.
If you integrate <img style="vertical-align: middle"
src="cid:part4.FA7D06D6.81C43908@mercer.edu"
alt="$\psi^*\psi$"> on that interval you will get one for the
probability. In other words there is a 100% probability of
finding the particle in the box.<br>
</font></p>
<p><font face="serif"><br>
</font></p>
<p><font face="serif">So, what if we want to find the probability of
finding the particle on the closed interval [0.32 a, 0.35 a]
then I set up the following integration.</font></p>
<p><font face="serif"><br>
</font></p>
<p><font face="serif"><img style="vertical-align: middle"
src="cid:part5.DEC39515.37C200FE@mercer.edu" alt="$\int_{0.32
a}^{0.35 a} \frac{2}{a} \sin^2\left(\frac{3 \pi x}{a}\right)
dx$"><br>
</font></p>
<p><br>
</p>
<p>Mathematica can do this integral easily, or you can use the
integral tables on page 1016 of your text. You should get a
small positive number.</p>
<p><br>
</p>
<p><br>
<font face="serif"></font></p>
<p><font face="serif"></font><br>
</p>
<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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