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4. Assume the particle is confined to a ring to explain a crude model for the electronic structure of benzene. The 2D Schrdinger Equation in polar coordinates is 22[r1r(rr)+r2122+U(r,)]=E.U(r,)=,forr=aU(a,)=0,forr=a (a) Explain why (r,)=0 for r=a. (5pt) (b) What is the simplified form of the Schrodinger Equation that applies when the particle is confined to the ring? (15pt) (c) Apply the periodic boundary condition that (a,)=(a,+2) to obtain the En energy level. Assume that particle is rotating in one direction. (10pt) (d) The CC bond length in benzene is 1.37A. Thus a circle that goes through all 6 carbon atoms has a radius r=1.397A. Use this to estimate the n=2<>