4.5 Legendre'sche Polynome

Eigenfunktionen des Drehimpulsoperators $\vec{L}^{2}_{}$ und $\vec{L_z}\,$ in der Quantenmechanik ^4.4

$$\leq \leq \infty {1 \over 2}$$ (4.26)

$${1 \over 2} {1 \over 2}$$ (4.27)

allgemein:

$${1 \over {2^n n!}} {d^n \over {dx^n}}$$ (4.28)

$${{(2n)!}\over{2^{2n}(n!)^2}} \pm \pm$$ (4.29)

Rekursionsformel:

(n + 1)P_{n + 1}(x) = (2n + 1)xP_n(x) - nP_{n - 1}(x) (4.30)

$${d^2 \over {dx^2}} {d \over {dx}}$$ (4.31)

$${{n(n+1)} \over {2n+1}}$$ (4.32)

$$\theta {4\pi \over {2 l + 1}} \sum_{m=-l}^{l} \overline{Y_l^m(\theta_1, \phi_1)} \theta_{2}^{} \phi_{2}^{}$$ (4.33)

$${1 \over {\vert\vec{r_1}-\vec{r_2}\vert}} {1 \over \sqrt{r_1^2+r_2^2+2 r_1 r_2 \cos(\gamma)}} \sum_{l=0}^{\infty} {r_<^l \over r_>^{l+1}} \gamma$$ (4.34)