Consider the wave function of a particle ψ(r)=(2x+2y+z)f(r), where f(r) is a spherically symmetric function.
(a) Is ψ(r) an eigenfunction of L^2? If so, what is the eigenvalue?
(b) What are the probabilities for the particle to be found in the state ml=−1, ml=0, and ml=1?
(c) If ψ(r) is an energy eigenfunction with eigenvalues E and if f(r)=3r2, find the expression of the potential V(r) to which this particle is subjected.