Editing Spherical harmonics (section)

===Condon–Shortley phase===
One source of confusion with the definition of the spherical harmonic functions concerns a phase factor of <math>(-1)^m</math>, commonly referred to as the [[Edward Condon|Condon]]–Shortley phase in the quantum mechanical literature. In the quantum mechanics community, it is common practice to either include this [[phase factor]] in the definition of the [[associated Legendre polynomials]], or to append it to the definition of the spherical harmonic functions. There is no requirement to use the Condon–Shortley phase in the definition of the spherical harmonic functions, but including it can simplify some quantum mechanical operations, especially the application of [[Ladder operator|raising and lowering operators]]. The geodesy<ref>Heiskanen and Moritz, Physical Geodesy, 1967, eq. 1-62</ref> and magnetics communities never include the Condon–Shortley phase factor in their definitions of the spherical harmonic functions nor in the ones of the associated Legendre polynomials.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Condon-Shortley Phase |url=https://mathworld.wolfram.com/Condon-ShortleyPhase.html |access-date=2022-11-02 |website=mathworld.wolfram.com |language=en}}</ref>