One very important concept and principle of quantum mechanics is the Pauli exclusion principle. Responsible for things such as different electron orbits, it can be observed in many places.

**The exclusion principle states that no two Fermions can occupy the same quantum state. **

But what does this mean?

This can be shown in terms of the wavefunction of the fermions, and in particular the wavefunction of a system comprising two neutrons. The wavefunction of a fermion describes mathematically its position and other such quantum properties.

According to the Pauli exclusion principle the following is true about the wavefunction (Ψ) of a composite system of positions of two fermions:

The formula above describes the fact that if the two neutrons are swapped, the composite wavefunction is multiplied my -1. However, if the wavefunction is the same for both:

However, the exclusion principle states that Ψ(n1,n2)= -Ψ(n2,n1). Thus for both the above to be true:

Therefore, it is mathematically impossible for 2 fermions to have the same wavefunction, and therefore occupy the same quantum state. Unless one (or both) the wave functions are equal to zero (meaning that they don't exist).

**I know the proof above is very basic, so I would love to learn how to properly prove it mathematically, I’m guessing something to do with the Schrödinger equation will help me? **

PlanckTime - Amin

A lot of proofs of this are wrong, but yours is sweet and simple. The meaning of the Pauli Exclusion is formally told as that the particles with half-integer spins, or fermions, are able to be described by anti-symmetric wave functions, or a wave function that has (a,b) and not (b,a), and particles with an integer spin or bosons, will be described be a symmetric wave function, (a,b) and (b,a) are there. I described it quite simply here, and I am sure that you know spins and the asymmetric relation, but I just wanted to be more specific in describing it.

That one guy that's always on