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====== Normalizing Wave Functions ======

===== Prompt =====

** "Normalize one of the two following wave functions:" **

$$\psi(x) =
\begin{cases}
0, & \text{if $x$ < 0} \\
sin(\frac{\pi{x}}{L}), & \text{if  0 < $x$ < $L$}\\
0, & \text{if $x$ > $L$}
\end{cases}
$$

$$\psi(x) =
\begin{cases}
0, & \text{if} \; x < -\frac{L}{2} \\
cos(\frac{\pi{x}}{L}), & \text{if} \; -\frac{L}{2} < x < \frac{L}{2}\\
0, & \text{if} \; x > \frac{L}{2}
\end{cases}
$$



===== Context =====

This [[strategy:smallwhiteboard:|SWBQ]] can be used to open up discussions about the normalizing factor and why it is there.

===== Wrap Up =====
  * Discussion of the normalizing factor $\sqrt {\frac{2}{L}} $ (which has been encountered before in a Modern Physics course) and a realization of why it is there.  Also discuss its dimensions.   
  * Discussion of the need for specifying the wave function outside the box.
  * Discussion after the report back of the fact that the two forms represent the same wave function, but with a different origin of the well. Parity can be discussed here.


{{wvswnorm.ppt|Powerpoint slide}}
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{{wvswnorm.pdf|PDF slide}}

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