Though the particle in a box (infinite potential well) seems like a very unrealistic potential, it can actually be used to explain a bit about how humans see. The important light-absorbing molecule in human eyes is called retinal. Retinal consists of a chain of carbon atoms, roughly 1.5x10^-9mlong. An electron in this long chain molecule behaves very much like a particle in a box.

Find the wavelength λ_n of the photon that must be absorbed by an electron to move it from the n^th state of a box to the (n+1)^th state. Assume that the box has length L and that the electron has mass m.