2. For a time-independent quantum harmonic oscillator with mass m and characteristic frequency w = k/m, four operators are defined as follows: d d2 d2 dx Z1 = x -; Z2 =x2 "; 23 = X dx dx2 ; 24 = x2 dx2 A. Write Zi (j = 1, 2, 3, 4) in terms of raising and lowering operators. You do not have to simplify these expressions at this point. B. Find the expectation values of Z; (j = 1, 2, 3, 4) for the no stationary states of the oscillator