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.
Best Answer
You seem to be mixing the spin and the orbital angular momentum. The classical counterpart of the orbital angular momentum, is the the angular momentum you would obtain from the electron orbiting around the proton. It is called orbital because it is related to the orbital degrees of freedom, that you are discussing in your course.
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.
The idea that the electron is a spinning ball, is a common way to explain the spin and not the angular momentum. Note that even this case, it is a wrong interpretation of the spin. The electron is not a ball. It is not a point like object, otherwise it would be a particle. The electron is both a wave and a particle, and It is described by a wave function.