CONSERVATION OF ANGULAR MOMENTUM IN QUANTUM MECHANICS

The recent two papers have successively proposed the concepts and more precise expressions of strict conservation or statistical conservation of physical quantities, which are different from the expression of a conserved quantity in quantum mechanics. The Hamiltonian operator of the system discussed in this paper are independent of time, so it is commutative with the operators of an angular momentum itself, its component and its square, so that all these quantities are conserved quantities. In an isolated composite system, one of the angular momentum components of the total system are strictly conserved, while the angular momentum components of the subsystems can only be conserved statistically, both of which can be expressed in terms of eigenvalues and eigenfunctions. Generally, angular momentum itself does not have eigenvalues and eigenfunctions, so it cannot be expressed as strict conservation in terms of these concepts. Although there are eigenvalues and eigenfunctions for the square of angular momentum, they cannot express strict conservation either. And they can only be expressed as statistical conservation.