2.16 Consider a one-dimensional simple harmonic oscillator. a. Using α = ma 2ħ ip an x- = mw √√√nn − 1) a³|n)]¯¯ {√√n+1|n+1), evaluate (m|x|n), (mp|n), (m|{x,p}|n), (m|x2|\n), and (m|p²|n). b. Translated from classical physics, the virial theorem states that (x. VV) (3D) or m m dv (x) (1D) dx Check that the virial theorem holds for the expectation values of the kinetic and the potential energy taken with respect to an energy eigenstate.

2.16 Consider a one-dimensional simple harmonic oscillator. a. Using α = ma 2ħ ip an x- = mw √√√nn − 1) a³|n)]¯¯ {√√n+1|n+1), evaluate (m|x|n), (mp|n), (m|{x,p}|n), (m|x2|\n), and (m|p²|n). b. Translated from classical physics, the virial theorem states that (x. VV) (3D) or m m dv (x) (1D) dx Check that the virial theorem holds for the expectation values of the kinetic and the potential energy taken with respect to an energy eigenstate.