The eigenfunctions in Problem 2 can be written in the form nx,ny,nz(x,y,z)=nx(x)ny(y)nz(z), with ni=0,1,2,. Suppose the oscillator was initially prepared in the state corresponding to (x,y,z;0)210(x)0(y)0(z)+211(x)0(y)0(z)+210(x)1(y)0(z) Determine as functions of time (a) the expectation value of the energy, (b) the expectation values of x,y, and z, and of x2,y2, and z2, (c) and the probabilities for observing the system in the eigenstates (nx,ny,nz) i. (0,0,0), ii. (1,0,0), iii. (0,1,0), iv. (0,0,1), v. (137,0,0)