1. The problem statement, all variables and given/known data We have an observable A, that has eigen vectors l a1 > and l a2 > , with eigenvalues a1 and a2 respectively. A second observable B has eigenvectors l b1 > and l b2 > with eigenvalues b1 and b2 respectively. The eigenstates of B can be written in terms of the eigenstates of A as: l b1 > = 3/4 l a1 > + sqrt(7)/4 l a2 > l b2 > = -sqrt(7)/4 l a1 > -3/4 l a2 > If the particle is in state l b2 > , what are the expectation values <A> and <B> in terms of a1, a2, b1 and b2 2. Relevant equations 3. The attempt at a solution expectiation value of, say A, is given by: <A> = <b2 l A l b2 > since the particle is in the state b2 now how do I proceed to find <A> ? Is A a 2x2 matrix?