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| -rw-r--r-- | buch/papers/kugel/spherical-harmonics.tex | 13 |
1 files changed, 11 insertions, 2 deletions
diff --git a/buch/papers/kugel/spherical-harmonics.tex b/buch/papers/kugel/spherical-harmonics.tex index 72f7402..5d394a9 100644 --- a/buch/papers/kugel/spherical-harmonics.tex +++ b/buch/papers/kugel/spherical-harmonics.tex @@ -639,8 +639,17 @@ quasi-normalization). where $m, n \in \mathbb{Z}$ and $|m| < n$. \end{definition} -However, for our purposes we will mostly only need the orthonormal spherical -harmonics. So from now on, unless specified otherwise, when we say spherical +Additionally, there is another quirk in the literature that should be mentioned. +In some other branches of physics such as seismology there is a so called +Condon-Shortley phase factor $(-1)^m$ in front of the square root in the +definition of the normalized spherical harmonics. It is yet another +normalization that is added for reasons that are not very relevant to our +discussion, but we are mentioning its existence since many numerical packages +(such as \texttt{SHTOOLS} \kugeltodo{Reference}) offer an option to add or +remove it from the computation. + +Though, for our purposes we will mostly only need the orthonormal spherical +harmonics, so from now on, unless specified otherwise when we say spherical harmonics or write $Y^m_n$, we mean the orthonormal spherical harmonics of definition \ref{kugel:def:spherical-harmonics-orthonormal}. |