1. At t = 0, the quantum particle is describe by the localized wave packet Ala|z]) ;|z| (1) de? or (a) (6 pts) Prove equation (1). Suppose that the particle is subject to the potential V(x) = Eliaa::', where a is a positive constant. The classical equation of motion for this particle is mi + az? = (. (b) (3 pts) Using equation (1) derive the equation of motion for (z) for this particle. Express the equation in terms of m, a, and the variance (Az)? in position. () (1 pt) Compare the equation of motion for (z) obtained in item 1b to the classical equation of motion. How do they differ? 3. At t = 0, a quantum particle bounded in an infinite square well of width a is prepared in a state described by the wave function (z.,0) Az(a+z)(a2z) :0