Q#09. Let t4, (x) denote the orthonormal stationary states of a system corresponding to the energy En. Suppose that the normalized wave function of the system at time t = 0 is p(x,0) and suppose that a measurement of the energy yields the value E1 with probability 1/2, E2 with probability 3/8, and E3 with probability 1/8. (a) Write the most general expansion for 4(x,0) consistent with this information. (b) What is the expansion for the wave function of the system at time 1, Þ(x, t)? (c) Show that the expectation value of the Hamiltonian does not change with time.

Q#09. Let t4, (x) denote the orthonormal stationary states of a system corresponding to the energy En. Suppose that the normalized wave function of the system at time t = 0 is p(x,0) and suppose that a measurement of the energy yields the value E1 with probability 1/2, E2 with probability 3/8, and E3 with probability 1/8. (a) Write the most general expansion for 4(x,0) consistent with this information. (b) What is the expansion for the wave function of the system at time 1, Þ(x, t)? (c) Show that the expectation value of the Hamiltonian does not change with time.