Answer to Question #101101 in Quantum Mechanics for TIP

Question

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

Answer 1

A constant of motion in mechanics is a quantity that is conserved throughout the motion. If we measure all components of the angular momentum simultaneously, we cannot obtain their definite values. However, it is possible to find simultaneous eigenfunctions of $\vec{L}^2$ and only one of its components, thus we can find both the magnitude of the angular momentum and one of its components. This way the angular momentum can be fully specified and conserved.

That is why L² and only one of its components are regarded as a constant of motion.