No, NOT like the Pauli matrices. The Pauli matrices are the generators. I'm referring to the matrix functions that represent finite rotations. They are functions in the sense that they are functions of the three Euler angles. And they are eigenfunctions of S and Sz.Like the Pauli matricies Sx, Sy, Sz, I know the eigenvalues/eigenvectors, but what are the eigenfunctions?
The spin operator is a mathematical operator used in quantum mechanics to describe the intrinsic angular momentum of a particle. It is represented by the symbol S and is a vector operator that gives information about the direction and magnitude of a particle's spin.
Eigenfunctions of spin operator are important in quantum mechanics because they represent the possible states of a particle's spin. These eigenfunctions are also known as spin states and are used to describe the spin of particles such as electrons, protons, and neutrons.
Eigenfunctions of spin operator are directly related to spin measurements. When a spin measurement is performed on a particle, the result is an eigenvalue of the spin operator. The corresponding eigenfunction represents the state of the particle's spin after the measurement.
Spin up and spin down states are two possible eigenfunctions of the spin operator. They represent the two opposite directions of a particle's spin, with spin up being aligned with the direction of the spin operator and spin down being aligned in the opposite direction.
The eigenfunctions of spin operator can be calculated using mathematical techniques such as matrix diagonalization or the use of ladder operators. These methods help to find the possible spin states and their corresponding eigenvalues for a given particle.