5. A particle of mass m has wavefunction (x) Ae-2/2L2 and total energy E = h²/2mL², where L is a length. = (a) Find the potential energy V as a function of x. What is the classical potential that has this dependence? (b) Find the kinetic energy K as a function of x.

A particle is described by the wavefunction Ψ(t, x), and the momentum operator is denoted by pˆ. a)  Write down an expression for the differential operator pˆ. b)  Write down an expression for the expectation value of the momentum, ⟨p⟩. c)  Write down an expression for the probability density, ρ. d)  Write down an expression for the probability of finding the particle between x = a and x = b.