Writing sin^2 theta * Sin 2 phi in terms of spherical Harmonics

[Physicslad78]

I am trying to write the term "Sin^2 theta * Sin 2 phi" in terms of spherical Harmonics (they form a combination of Y(2,-2) and Y(2,2)) but the term I get contains the imaginary number 'i'. Am I doing something wrong.. In fact this term is a part of a Hamiltonian and when I get the eigenvalues I find that some are complex! What is happening?


Thanks

 

[malawi_glenn]

It is very hard to tell what you are doing wrong if you don't show explicit the work you have done and how you motivate the steps.