Angular Momentum Operator - Quantization

Quantization

See also: Azimuthal quantum number and Magnetic quantum number

In quantum mechanics, angular momentum is quantized – that is, it cannot vary continuously, but only in "quantum leaps" between certain allowed values. For any system, the following restrictions on measurement results apply, where is reduced Planck constant:

If you measure...	...the result can be...	Notes
Lz	, where	m is sometimes called "magnetic quantum number". This same quantization rule holds for any component of L, e.g. Lx or Ly. This rule is sometimes called spatial quantization.
Sz or Jz	, where	For Sz, m is sometimes called "spin projection quantum number". For Jz, m is sometimes called "total angular momentum projection quantum number". This same quantization rule holds for any component of S or J, e.g. Sx or Jy.
	, where	L2 is defined by . is sometimes called "azimuthal quantum number" or "orbital quantum number".
	, where	s is called spin quantum number or just "spin". For example, a spin-½ particle is a particle where s=½.
	, where	j is sometimes called "total angular momentum quantum number".
and simultaneously	for, and for where and	(See above for terminology.)
and simultaneously	for, and for where and	(See above for terminology.)
and simultaneously	for, and for where and	(See above for terminology.)