In this problem you are asked to solve the schrödinger equation for a particle of mass m constrained to move on a circle of radius r with a polar angle θ 2mr2d62 (i) what is the boundary condition? hint: what happens to if the angle goes a full circle? (ii) apply the boundary condition to find the wave functions ψ(θ) and the corresponding energies e; specify the range of any discrete values in your result. hint: it may be easier to work with complex functions. (iii) apply this model to benzene by assuming 6 mobile electrons moving on a ring with a radius of 1.39 a. calculate the wavelength (in nm) of the lowest-energy electronic transition. in what region of the electromagnetic spectrum is this?