Cascaded quantum measurementsAn operatorˆA, representing observableA, has two normalized eigenstates|ψ1〉and|ψ2〉, with eigenvaluesa1anda2, respectively. OperatorˆB, representing observableB, has two normalized eigenstates|φ1〉and|φ2〉, with eigenvaluesb1andb2.The eigenstates are related by|ψ1〉=15(3|φ1〉+ 4|φ2〉),|ψ2〉=15(4|φ1〉−3|φ2〉).(1)(a) Show that if|φ1〉and|φ2〉are properly normalized, so are|ψ1〉and|ψ2〉.(b) ObservableAis measured, and the valuea1is obtained. What is the state of thesystem immediately after this measurement?Hint: note that I did not tell youwhat the state of the system was before the measurement. Does it matter?(c) Immediately after the measurement ofAfounda1,Bis now measured. What arethe possible results, and what are their probabilities?(d) Right after the measurement ofB, Ais measured again. What is the probabilityof gettinga1?Hint: note that I did not specify which value ofbwas obtained, soyour calculation has to allow for the possibility that either one was