3) a) (5 pts) Show by symbolic integration that the optical transition probability for optical excitation from the n=1 to the n=2 state of a one-dimensional square quantum well of side L and infinite walls is finite and the probability is zero for excitation from the n=1 to n=3 state. b) (5 pts) Repeat these calculations by numerical integration (Simpson's rule or better approximation) and find the ratio of the smaller to larger of the two integrals for an integration of 1000 steps across the well. Include a copy of the code you wrote to complete these integrations. 3) a) (5 pts) Show by symbolic integration that the optical transition probability for optical excitation from the n=1 to the n=2 state of a one-dimensional square quantum well of side L and infinite walls is finite and the probability is zero for excitation from the n=1 to n=3 state. b) (5 pts) Repeat these calculations by numerical integration (Simpson's rule or better approximation) and find the ratio of the smaller to larger of the two integrals for an integration of 1000 steps across the well. Include a copy of the code you wrote to complete these integrations