Quantum Physics For Dummies, Revised Edition
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Infinite square well, in which the walls go to infinity, is a favorite problem in quantum physics. To solve for the wave function of a particle trapped in an infinite square well, you can simply solve the Schrödinger equation.

Take a look at the infinite square well in the figure.

A square well.
A square well.

Here’s what that square well looks like:

image1.png

The Schrödinger equation looks like this in three dimensions:

image2.png

Writing out the Schrödinger equation gives you the following:

image3.png

You’re interested in only one dimension — x (distance) — in this instance, so the Schrödinger equation looks like

image4.png

Because V(x) = 0 inside the well, the equation becomes

image5.png

And in problems of this sort, the equation is usually written as

image6.png

So now you have a second-order differential equation to solve for the wave function of a particle trapped in an infinite square well.

You get two independent solutions because this equation is a second-order differential equation:

image7.png

A and B are constants that are yet to be determined.

The general solution of

image8.png

is the sum of

image9.png

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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