Suppose that t and v are the kinetic and potential energies, and and momentum. and p are the position (a) prove that [pq, r where p, q and r are operators p[q, r] + [p, r\q, _ (b) show that [f(x), p] = ih dr for an arbitrary function f(x) (c) show that (xp) 2 (t) (1) dt dr (d) show that the left side of eq. (1) becomes zero in a stationary state to obtain dv 2 (t) dar which is called the virial theorem. (e) use the virial theorem, prove that (t) = (v) for stationary states of the harmonic oscillator