# What is the angular momentum of an electron? And how can it be zero?

I'm in my first undergrad physics series and we're learning a bit about quantum mechanics. We've been studying the hydrogen atom in it's ground state. We're using the time independent Schrodinger equation, but have only made qualitative assessments.

I am a bit confused about angular momentum. The book never explicitly states exactly what it is. It seems a bit different from the angular momentum we studied for big classical objects. I've been imagining the electron as a spinning ball of charge and the angular momentum is analogous to the angular momentum of a large spinning object, but I'm starting to think that's incorrect. I've also been told the electron is a point object, which conflicts with my understanding of angular momentum.

Additionally it is confusing to me that, knowing the electron never ceases to spin, angular momentum could ever be zero, but that seems to be the case for the $l$ = 0.

• Your textbook is talking about orbital angular momentum, which is exactly the same momentum you studied for classical objects. The electron orbits the nucleus, thus has angular momentum (from the reference point of the nucleus). The electron spinning has nothing to do with the angular momentum you're talking about. May 23, 2018 at 14:56
• This is a bit that's confusing me too. We talk about this L vector as if it orbits around the Z axis.. but then we also say that the electron exists on surfaces that describe high probability.. and that the orbital model (as in how planets orbit the sun) is incorrect. Either way, thank you for helping to clarify my question. I think I have some things I can ask my instructor now. May 24, 2018 at 16:38

You are trying to connect quantum mechanics with classical mechanics. This is not an easy task, and understanding the classical behavior from the quantum behavior is a tedious task in some cases. In any case you can only connect quantum mechanics to classical mechanics, when talking about averages. In your case, you connect the classical angular momentum with the average of some operator over the quantum state. The fact that $l=0$, means that the electron has on average a zero angular momentum. The exact definition of the orbital angular momentum operator is given in any standard quantum mechanics text book, you can see for example this link on Wikipedia.