The virial theorem of classical mechanics applied to a single 1d particle subject to a force f(x) = −v 0 (x) in the potential v (x) is1 : 2 hti t = − hxf(x)i t = hxv 0 (x)i t , where h. .i t represents an average over time. in this question, you will develop the quantum mechanics analog of the virial theorem. (a) use the following result for an arbitrary state |ψi and matrix q that is not explicitly time dependent ( ∂q ∂t = 0) d hqiψ dt = i ~ h[h, q]iψ to show that d hxpiψ dt = 2 htiψ − hxv 0 iψ , where t = p 2/(2m) is the usual kinetic energy and v 0 = v 0 (x). note that q = xp is not hermitian, but the result above does not assume this