If we use the column vector representation of the various spin eigenstates above, then we can use the following representation for the spin operators: You can verify that this is a good representation...If we use the column vector representation of the various spin eigenstates above, then we can use the following representation for the spin operators: You can verify that this is a good representation of the spin operators by making sure that all all of the various observations about spin states are reproduced by using these operators and these vectors to predict them from the theory.
Because spin is a type of angular momentum, it is reasonable to suppose that it possesses similar properties to orbital angular momentum. Thus, by analogy, we would expect to be able to define three o...Because spin is a type of angular momentum, it is reasonable to suppose that it possesses similar properties to orbital angular momentum. Thus, by analogy, we would expect to be able to define three operators that represent the three Cartesian components of spin angular momentum. Moreover, it is plausible that these operators possess analogous commutation relations to the three corresponding orbital angular momentum operators.
