In a semiconductor, an electron and a hole, which have opposite charges -e and e, respectively, attract each other to form bound states called exciton states. In the solid, the electron and the hole have effective mass m_(e)^(**)~~0.1m_(e) and m_(h)^(**)~~0.4m_(e), respectively, with m_(e) denoting the mass of an electron in vacuum. The Coulomb force between the electron and the hole in the solid, which is a dielectric with relative permittivity epsi_(r)~~10, is F=-(r)/(r)xx(e^(2))/(4piepsi_(0)epsi_(r)r^(2)) where epsi_(0) is the vacuum permittivity, and r is the displacement of the electron from the hole. (a) Write down the Hamiltonian for the relative motion between the electron and the hole and determine all its eigenenergies and the degeneracies. (Hint: Consider the typical length scale and energy scale of the exciton in comparison with those of hydrogen atoms.) (16 marks) (b) The uncertainty of the coordinate of the electron relative to the proton in a hydrogen atom is known to be Ax ~ 0.5 10-10 m when the atom is in its ground state. What are the expectation value (y) and uncertainty Ay of the y coordinate of the electron relative to the hole when the exciton is in its ground state? (6 marks)