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jishnub / SphericalHarmonics.jl

Associated Legendre Polynomials and Spherical Harmonics in Julia
MIT License
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Condon-Shortley Phase Factor #93

Open svvelamp opened 2 years ago

svvelamp commented 2 years ago

According to the documentation for Plm (https://docs.juliahub.com/SphericalHarmonics/NjDk0/0.1.14/#SphericalHarmonics.computePlmcostheta-Tuple{Any}) and for the spherical harmonics Ylm (https://docs.juliahub.com/SphericalHarmonics/NjDk0/0.1.14/#SphericalHarmonics.computeYlm ) the C-S factor (-1)^m is not included in the definitions. However, that's not what I am observing. For example, the formula for Y21 with the C-S factor is given by

Y21 (theta, phi) = (-)sqrt(15/32pi) sin(2*theta) exp(i phi).

For theta=pi/3, phi=0, it gives a value of -0.3345232717786446.

Now following code produces exactly the same value: ynm = computeYlm(pi/3,0.0,lmax=2); ynm[(2,1)] -0.33452327177864466 - 0.0im

I have verified the same behavior for Y(1,1) as well.

Is it possible that the documentation is incorrect? Or am I missing something? [I can think of another possibility, the branch used in defining (1-x^2)^{m/2}) in the definition of Pnm.]

Could you please clarify?

Thanks, Sanjay Velamparambil

svvelamp commented 2 years ago

One follow-up: in the cited reference by Limpanuparb and Milthorpe , the definition of Plm does include a factor of (-1)^m.

jishnub commented 2 years ago

Yes, the docs were incorrect there. The phase factor is, in fact, included. The docs are updated now

svvelamp commented 2 years ago

thank you!

From: Jishnu Bhattacharya @.> Sent: Saturday, April 30, 2022 12:26 PM To: jishnub/SphericalHarmonics.jl @.> Cc: Sanjay Velamparambil @.>; Author @.> Subject: Re: [jishnub/SphericalHarmonics.jl] Condon-Shortley Phase Factor (Issue #93)

[External Sender]

Yes, the docs were incorrect there. The phase factor is, in fact, included. The docs are updated nowhttps://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fjishnub.github.io%2FSphericalHarmonics.jl%2Fdev%2F%23SphericalHarmonics.computePlmcostheta-Tuple%257BAny%257D&data=05%7C01%7Csanjay.velamparambil%40ansys.com%7C561cb1790e61457933ec08da2ad6fa95%7C34c6ce6715b84eff80e952da8be89706%7C0%7C0%7C637869400116373777%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=lnYC6FUxT0DA2QlNqlgXkqY6VFVXpCWaRiCu4SuYxe4%3D&reserved=0

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