Angular momentum of electron

[sir c.v.raman]

Homework Statement

What is the significance of quantization of angular momentum in the absence of magnetic field?

Homework Equations

Lz=mlh/2∏;Jz=mjh/2∏;Sz=msh/2∏.

The Attempt at a Solution

I read that in the absence of magnetic field,z-axis direction is arbitrary and the component of L along whatever direction we choose must be mlh/2∏.How can this be true?Moreover I think, say in 2p state,each of the 3 ml values(-1,0,1)are assigned to uniquely to each of 2px,2py and 2pz.This is also not in accordance with space quantization concept.
Please anyone explain this to me.

 

[Adrmay]

The quantization of angular momentum in the absence of a magnetic field is important because it allows us to understand the behavior of atomic systems. When an atom is in a state with no external applied fields, the angular momentum of the system about any axis is still quantized. This means that the atom can only occupy certain energy levels and have certain possible orientations. This is because the angular momentum of the system must be a multiple of h/2π, where h is Planck's constant. This quantization of angular momentum is important in understanding the behavior of atoms and molecules in different states.