Expression des harmoniques sphériques.

Nous donnons ci dessous l'expression de quelques $Y_\ell^m$ pour $\ell \leq 3$

$$Y_0^0 = \sqrt{ 1 \over 4 \pi}$$ (2.77)

$$Y_1^0 = \sqrt{ 3 \over 4 \pi} \cos \theta \hskip 2 cm Y_1^{\pm 1} = \sqrt{ 3 \over 8 \pi} \sin \theta \exp{\pm \imath \phi}$$ (2.78)

$$Y_2^0 = \sqrt{ 5 \over 16\pi} (3\cos^2 \theta - 1) \hskip 2 ... ...{15 \over 8 \pi} \sin \theta \cos \theta \exp{\pm \imath \phi}$$ (2.79)

$$Y_2^{\pm 2} = \sqrt{15 \over 32\pi} \sin^2 \theta \exp{\pm \imath 2\phi}$$ (2.80)

$$Y_3^0 = \sqrt{ 7 \over 16\pi} (5\cos^3 \theta - 3\cos \theta... ...r 64\pi} \sin \theta (5\cos^2 \theta -1) \exp{\pm \imath \phi}$$ (2.81)

$$Y_3^{\pm 2} = \sqrt{105 \over 32\pi} \sin^2 \theta \cos\thet... ...= \sqrt{ 35 \over 64\pi} \sin^3 \theta \exp{\pm \imath 3\phi}$$ (2.82)

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