Quantum Physics For Dummies, Revised Edition
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In your quantum physics course, you may be asked to normalize the wave function in a box potential. Here's an example: consider the wave function

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In the x dimension, you have this for the wave equation:

image1.png

So the wave function is a sine wave, going to zero at x = 0 and x = Lz. You can also insist that the wave function be normalized, like this:

image2.png

By normalizing the wave function, you can solve for the unknown constant A. Substituting for X(x) in the equation gives you the following:

image3.png

Therefore,

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which means you can solve for A:

image5.png

Great, now you have the constant A, so you can get X(x):

image6.png

Now get

image7.png

You can divide the wave function into three parts:

image8.png

By analogy with X(x), you can find Y(y) and Z(z):

image9.png

So

image10.png

equals the following:

image11.png

That's a pretty long wave function. In fact, when you're dealing with a box potential, the energy looks like this:

image12.png

About This Article

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About the book author:

Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

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