Quantum Physics For Dummies, Revised Edition
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In quantum physics, you can find the wave function of the ground state of a quantum oscillator, such as the one shown in the figure, which takes the shape of a gaussian curve.

The ground state of a quantum mechanical harmonic oscillator.
The ground state of a quantum mechanical harmonic oscillator.

As a gaussian curve, the ground state of a quantum oscillator is

image1.png

How can you figure out A? Wave functions must be normalized, so the following has to be true:

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Substituting for

image3.png

gives you this next equation:

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You can evaluate this integral to be

image5.png

Therefore,

image6.png

This means that the wave function for the ground state of a quantum mechanical harmonic oscillator is

image7.png

Cool. Now you’ve got an exact wave function.

About This Article

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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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