[SciPy-Dev] Spherical harmonics, convention

Ralf Gommers ralf.gommers@googlemail....
Sat Mar 20 03:52:00 CDT 2010

On Sat, Mar 20, 2010 at 1:50 AM, Matthew Brett <matthew.brett@gmail.com>wrote:

> Hi,
> I noticed that scipy.special.sph_harm uses conventions that (on
> superficial reading) seem to be rather unusual; can I ask for advice
> whether that is correct?

> For example; http://en.wikipedia.org/wiki/Spherical_harmonics assumes:
> theta = polar angle
> phi = azimuthal angle
> l (little L) = degree of harmonic
> but we have:
> theta = azimuthal angle
> phi = polar angle
> n = degree of harmonic
> I realize that the theta / phi switch is the difference between
> physics and math conventions of spherical coordinates, but my
> superficial impression was that there was a rather strong tradition in
> spherical harmonics to prefer theta = polar, phi = azimuthal; is that
> correct?

It indeed looks weird to me as a physicist, I've never seen it the 'wrong'
way around. But I have to admit that I don't know how widely spherical
harmonics are used in mathematics, and for what. I associate them with the
hydrogen atom, multipole expansions in electrodynamics, etc.

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