Quantum Physics For Dummies, Revised Edition
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In quantum physics, if you are given the wave equation for a particle in an infinite square well, you may be asked to normalize the wave function. For example, start with the following wave equation:

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The wave function is a sine wave, going to zero at x = 0 and x = a. You can see the first two wave functions plotted in the following figure.

Wave functions in a square well.
Wave functions in a square well.

Normalizing the wave function lets you solve for the unknown constant A. In a normalized function, the probability of finding the particle between

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adds up to 1 when you integrate over the whole square well, x = 0 to x = a:

image3.png

Substituting for

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gives you the following:

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Here’s what the integral in this equation equals:

image6.png

So from the previous equation,

image7.png

Solve for A:

image8.png

Therefore, here’s the normalized wave equation with the value of A plugged in:

image9.png

And that’s the normalized wave function for a particle in an infinite square well.

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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