Quantum Physics For Dummies, Revised Edition
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Infinite square wells, in which the walls go to infinity, are a favorite in quantum physics problems. In some instances, you may want to shift things so that the square well is symmetric around the origin.

For example, the standard infinite square well looks like this:

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But what if you want to move the square well so that it extends from

image1.png

Here's what the new infinite square well looks like in this case:

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You can translate from this new square well to the old one by adding a/2 to x, which means that you can write the wave function for the new square well in this equation as follows:

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Doing a little trig gives you the following equations:

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So as you can see, the result is a mix of sines and cosines. The bound states are these, in increasing quantum order:

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And so on.

Note that the cosines are symmetric around the origin:

image6.png

The sines are anti-symmetric:

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About This Article

This article is from the book:

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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