Consider a particle of mass m in a three-dimensional cubic infinite well of side a: V (x, y, 2 ) = 0 for O Ex, y, z Sa co otherwise The wavefunction of this particle at f = 0 is given by the following superposition of the eigenfunctions Wynn, (x, y, Z): y (x, y, z) = A (61/1,1,1 - 34/2,1,1 + 9451,2,3) Recall that for this particle, the energy eigenvalues are Emptying = (n + n + n?) e where e = 2ma2 Answer the following questions without performing any actual integrations but using the orthonormality property of the eigenfunctions: -00 -00 -00 where on "' is the Kronecker delta function. a. Find the normalization constant A. Answer: A = 31/14 b. i. What is the probability of finding the system in the state with energy 3c ? Answer: 2/7 ii. What is the probability of finding the system in the state with energy 6c ? Answer: 1/14 iii. What is the probability of finding the system in the state with energy 12c? Answer: 0 iv. What is the probability of finding the system in the state with energy 14c ? Answer: 9/14 c. What is the expectation value of the energy? Answer: X3+-X6+-X14 6= 10.286e