7.3 Exercise 1

A particle with mass m is moving along the x-axis in a potential given by the potential energy function $U \left(x\right) = 0.5 m \omega^{2} x^{2}$. Compute the product $\Psi \left(x , t\right)^{\star} U \left(x\right) \Psi \left(x , t\right) .$ Express your answer in terms of the time-independent wave function, $\psi \left(x\right) .$