Quantum Physics For Dummies
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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


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


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


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


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


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

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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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