Quantum Physics For Dummies, Revised Edition
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At some point, your quantum physics instructor may want you to find the total energy equation for three-dimensional free particle problems. The total energy of the free particle is the sum of the energy in three dimensions:

E = Ex + Ey + Ez

With a free particle, the energy of the x component of the wave function is

image0.png

And this equation works the same way for the y and z components, so here’s the total energy of the particle:

image1.png

Note that kx2 + ky2 + kz2 is the square of the magnitude of k — that is,

image2.png

Therefore, you can write the equation for the total energy as

image3.png

Note that because E is a constant, no matter where the particle is pointed, all the eigenfunctions of

image4.png

are infinitely degenerate as you vary kx, ky, and kz.

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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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