Then you have to understand what each one of those does to the each atomic orbital:
- total angular momentum: determined by the azimuthal quantum number
- angular momentum in one direction ( by convention): determined by the magnetic quantum number
There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
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In quantum mechanics, the angular momentum operator is an important operator that describes the angular momentum of a quantum system, similar to how the linear momentum operator describes the linear momentum. Angular momentum is a key concept in both classical and quantum physics, and it plays a crucial role in the behavior of atomic and subatomic particles. There are several forms of angular momentum in quantum mechanics, including orbital angular momentum and spin angular momentum.