So the point of introducing this odd-looking representation of the lowering operator is that the sin1−lθ term in the middle is exactly canceled when the operator is applies twice, and sim...So the point of introducing this odd-looking representation of the lowering operator is that the sin1−lθ term in the middle is exactly canceled when the operator is applies twice, and similar cancellations occur on repeating the operation, giving the (relatively) simple representation: Yml(θ,ϕ)=cl√(l+m)!(2l)!(l−m)!eimϕsin−mθdl−md(cosθ)l−msin2lθ
