Sequential measurements. An operator , representing observable A, has two normalized eigen...

Sequential measurements. An operator , representing observable A, has two normalized eigenstates ψ1 and ψ2, with eigenvalues a1 and a2, respectively. Operator , representing observable B, has two normalized eigenstates ϕ1 and ϕ2, with eigenvalues b1 and b2. The eigenstates are related by

(a) Observable A is measured, and the value a1 is obtained. What is the state of the system (immediately) after this measurement?

(b) If B is now measured, what are the possible results, and what are their probabilities?

(c) Right after the measurement of B, A is measured again. What is the probability of getting a1? (Note that the answer would be quite different if I had told you the outcome of the B measurement.)