From Townsend Quantum Mechanics. Please write neatly and answer all parts!!

14.13. (a) Show for the one-dimensional harmonic oscillator that the position and mo- mentum operators in the Heisenberg picture are given by * H (1) = *H(0) cos wt + PXH(0) sin wt ma Pxy (1) = Px (0) cos wt - mox H (0) sin wt respectively, where *#(0) = x is the usual position operator in the Schrodinger picture and Px (0) = px is the usual momentum operator in the Schrodinger picture. (b) Show that the equal time commutator of the position and momentum operators in the Heisenberg picture is given by [RH(1), Pxo (1) ] = ih What happens if times for the two operators are different