# Fermions and Pauli Exclusion Principle

I started to study quantum ideal gas and I am reading Salinas "Introduction to Statistical Physics". In chapter 8 , he states that when speaking of fermions, only one particle can occupy an orbital(particle with same quantum numbers), which obeys the Pauli exclusion principle. My doubt is related to the fact, that, according to the Pauli exclusion principle, in an orbital I need to have two particles, for example electrons, with the opposite spins, so that means there are two particles in the same orbital with different quantum states, right? The number of orbitals aren't defined by the quantum number spin, but the quantum states are. So that means that I can have more than one electron in an orbital with different quantum states? I am just starting to study quantum mechanics and statistical physics so I'm trying to understand the concepts as well as I possibly can.

## 1 Answer

I don't know the exact wording of your book, but "only one particle can occupy an orbital" is wrong.

The Pauli exclusion principle states that no two fermions can be in the same quantum state, that is to say they cannot both have the exact same set of quantum numbers.

An orbital is defined by the $$n, \ell,$$ and $$m_\ell$$ quantum numbers. So you can have as many fermions in it as additional quantum numbers that would distinguish them allow it. In the case of electrons, their spin can be either up or down, $$m_s = \pm 1$$, so you can only have two of them in the same orbital.

• The books says "same orbital (that is, with the same set of quantum numbers)". Thats why I got confused . But thanks now I understand better. thank you! Mar 31, 2021 at 20:15
• @AnaBranco Consider accepting the answer. Apr 4, 2021 at 21:39