3. This is a continuation of previous problem. (a) Compute ly = 1, ily in spherical coordinates. Please employ Euler's formula to obtain the most elegant looking result. (b) Compute I- in spherical coordinates. This involves straightforward but cumbersome algebra. The most efficient calculation employs the operators I, and I. 4. Adopting the spherical system of coordinates (see Problem 2), write down explicit expressions for (a) the Lame coefficients, (b) Vo, the gradient of a function q, given the unit vectors e, e, and e.. (c) V . a, the divergence of a vector a, given the components a, a,, and a (d) A'T, the Laplacian of a function "P. In parts (c) and (d) make sure to simplify your results as much as possible. 5. (a) Present your result for the Laplacian found in previous problem in a form that employs the operator 12 evaluated in Problem 3b. 2 (b) Classical Hamiltonian function of a free particle of mass m in spherical coordinates has the form H = - PF + (1) 2m 2mr2 where p, is the radial component of the particle momentum while M is the vector of its angular momentum. Given that the square of the momentum operator is p' = - PA (2) determine the form of the operator of radial momentum p