The initial state of a system is given in terms of four orthonormal energy eigenfunctions 1, 2, 3, and 4 as follows: 0t0

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The initial state of a system is given in terms of four orthonormal energy eigenfunctions 1, 2, 3, and 4 as follows:
0t01 12121 3214 36
(a) If the four kets 1, 2, 3, and 4 are eigenvectors to the Hamiltonian H with energies E1, E2, E3, and E4, respectively, find the state t at any later time t.
(b) What are the possible results of measuring the energy of this system and with what probability will they occur?
(c) Find the expectation value of the system’s Hamiltonian at t 0 and t 10 s.