The classical probability distribution function for a particle in an infinite one-dimensional well of length L is P=1/L. (a) Show that the classical expectation value of x^2 for a particle in an infinite one-dimensional well of length L that is centered at the origin is L^2/12. (b) Find the quantum expectation value of x^2 for the nth state of a particle in the one-dimensional box and show that it approaches the classical limit L^2/12 as n approaches infinity.