An operator Aˆ , representing observable A, has two normalized eigenstates ψ1 and ψ2, with eigenvalues a1 and a2, respectively. Operator Bˆ , representing observable B, has two normalized eigenstates φ1 and φ2, with eigenvalue b1 and b2. The eigenstates are related by
ψ1 =(3φ1 +4φ2 )/5, ψ2 =(4φ1 -3φ2 )/5.
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 a measurement of B, in which the value b1 is obtained, A is measured again. What is the probability of getting a1?