Answer to Question #101016 in Quantum Mechanics for Sahil

Question

Explain why L² and only one of its components are regarded as constant of motion.

Answer 1

It is impossible to measure all components of the angular momentum simultaneously, so we cannot obtain their definite values. However, one can find simultaneous eigenfunctions of $\vec{L}^2$ and only one of its components, therefore, which implies finding both the magnitude of the angular momentum and one of its components. This is enough to fully specify the angular momentum. When it is specified, it is conserved and can be regarded as a constant of motion.