2. (a) Give an account of the concept of electron spin and outline how its existence was verified experimentally in the Stern-Gerlach experiment. The Pauli spin matrices may be written as: 0 10 0 στ = (³) Oy = (5) 1 and σz = 0 =(5) −1 (b) Show that ( }) and ( 1 i ;) are eigenvectors of the operator Sy. Find the associated eigenvalues and normalisation constants. (c) Evaluate the expectation values (Sx), (Sy), (S2) and (S2) for a particle that has spin down in the y-direction. (d) A beam of spin-down particles, as determined by a Stern-Gerlach apparatus orientated in the y-direction, is passed through a Stern-Gerlach apparatus orientated in the x-direction. What are the probabilities of the possible results of the measurement of the spin along the direction of the x-axis?

2. (a) Give an account of the concept of electron spin and outline how its existence was verified experimentally in the Stern-Gerlach experiment. The Pauli spin matrices may be written as: 0 10 0 στ = (³) Oy = (5) 1 and σz = 0 =(5) −1 (b) Show that ( }) and ( 1 i ;) are eigenvectors of the operator Sy. Find the associated eigenvalues and normalisation constants. (c) Evaluate the expectation values (Sx), (Sy), (S2) and (S2) for a particle that has spin down in the y-direction. (d) A beam of spin-down particles, as determined by a Stern-Gerlach apparatus orientated in the y-direction, is passed through a Stern-Gerlach apparatus orientated in the x-direction. What are the probabilities of the possible results of the measurement of the spin along the direction of the x-axis?