Operators and commutation of operators

[solas99]

why is only one component of angular momentum is quantised, and what determines which component is quantised?

 

[shahbaznihal]

All components of Angular momentum are quantized but it is much easier to work with only the z component. And since space is isotropic, it does not really matter which direction you use. However, z component is simpler to work with mathematically.

 

[karlzr]

Different components of angular momentum do not commute, so they cannot be quantized at the same time. Of all the components, z component is the easiest to deal with.

 

[Jorriss]

Different components of angular momentum do not commute, so they cannot be quantized at the same time. Of all the components, z component is the easiest to deal with.

Do you mean can not be simultaneously diagonalized? All three are quantized simultaneously.