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Create Symmetric and Antisymmetric Wave Functions for a Three-or-More-Particle Systems

In quantum physics, you can put together the symmetric and antisymmetric wave functions of a system of three or more particles from single-particle wave functions. The symmetric wave function looks like this:

image0.png

And the antisymmetric wave function looks like this:

image1.png

This asymmetric wave function goes to zero if any two single particles have the same set of quantum numbers

image2.png

How about generalizing this to systems of N particles? If you have a system of N particles, the symmetric wave function looks like this:

image3.png

And the antisymmetric wave function looks like this:

image4.png

The big news is that the antisymmetric wave function for N particles goes to zero if any two particles have the same quantum numbers

image5.png
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