14. Consider a physical system whose state space, which is three-dimensional, is spanned by the orthonormal basis formed by the three kets u₁), u₂), U3). In this basis, the Hamiltonian operator H of the system and the two observables A and B are written: /0 1 6 : 9 :) 9 1 0 ΟΙ H = hwo 020 0 0 2 ; A =a0 0 0 0 1 0 1 0 ; B=b1 0 0 where wo, a and b are positive real constants. The physical system at time t = 0 is in the state: | 4(0)> = +112) +11%> 00 a. At time t = 0, the energy of the system is measured. What values can be found, and with what probabilities? Calculate, for the system in the state (0)), the mean value <H> and the root-mean-square deviation AH. b. Instead of measuring H at time t = 0, one measures A; what results can be found, and with what probabilities? What is the state vector immediately after the measurement? c. Calculate the state vector |(t)) of the system at time t. d. Calculate the mean values <A>(t) and <B>(t) of A and B at time t. What comments can be made? e. What results are obtained if the observable A is measured at time t? Same question for the observable B. Interpret.