  The derivation of spherical harmonics is the same in nearly every quantum
mechanics textbook and classroom. It is found to be difficult to follow, hard
to understand, and challenging to reproduce by most students. In this work, we
show how one can determine spherical harmonics in a more natural way based on
operators and a powerful identity called the exponential disentangling operator
identity (known in quantum optics, but little used elsewhere). This new
strategy follows naturally after one has introduced Dirac notation, computed
the angular momentum algebra, and determined the action of the angular momentum
raising and lowering operators on the simultaneous angular momentum eigenstates
(under $\hat L^2$ and $\hat L_z$).
