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](https://www.dummies.com/wp-content/uploads/396954.image0.png)
And the antisymmetric wave function looks like this:
![image1.png](https://www.dummies.com/wp-content/uploads/396955.image1.png)
This asymmetric wave function goes to zero if any two single particles have the same set of quantum numbers
![image2.png](https://www.dummies.com/wp-content/uploads/396956.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](https://www.dummies.com/wp-content/uploads/396957.image3.png)
And the antisymmetric wave function looks like this:
![image4.png](https://www.dummies.com/wp-content/uploads/396958.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](https://www.dummies.com/wp-content/uploads/396959.image5.png)