Define the eigenvalue equation (it is in the list of postulates) - students have seen that if the Stern-Gerlach beam is prepared in the |+>z state then the measurement will be +hbar/2
Argue from the above that there are two equations based on our knowledge of how to write the states and our Stern-Gerlach measurements, from which we can work backward and derive the matrix Sz that satisfies the eigenvalue equation
Then give the activity of having students find the matrices for Sx and Sy.
An alternative but longer version of this lecture and activity is given in the activity link on this topic.
Students are then shown general notation for the matrix representation of an arbitrary operator
Demonstrate solving for eigenvalues and eigenvectors with an example
Define the Pauli Spin matrices
Define the properties of Hermitian operators and give an example
Have students check the matrices for Sx, Sy and Sz to see if they are Hermitian and tie back to the postulates