A spin 3/2 nucleus situated at the origin is subjected to an external inhomogeneous electric field. The basic electric quadrupole interaction may be taken to be where ? is the electrostatic potential satisfying Laplace?s equation and the coordinate axes are so chosen that, show that the interaction energy can be written as and express A and B in terms of (?²? / ?x²)0 and so on. Determine the energy eigenkets (in terms |m>, where m = ? 3/2, ? ?) and the corresponding energy eigenvalues. Is there any degeneracy?

' ? 2s(s 1)h? ? Hint s? + s? + S? :? ) a 0. (38? -S?)+ (s? +52),