spins_unit_operators_and_measurements.ppt Pages 2-12

• 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