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Zugeordnete Kugelfunktionen

$ l=0$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-0_m-0}
$ P_0^0(\cos\theta)=1$
$ l=1$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-1_m-0}
$ P_1^0(\cos\theta)=\left( \cos \left( \theta \right) \right) ^{2}$
$ l=1$  
$ m=1$ \includegraphics[height=0.32\textheight]{maple/l-1_m-1}
$ P_1^1(\cos\theta)=\sqrt {1- \left( \cos \left( \theta \right) \right)
^{4}}$
$ l=2$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-2_m-0}
$ P_2^0(\cos\theta)=3/2  \left( \cos \left( \theta \right) \right)
^{4}-1/2$
$ l=2$  
$ m=1$ \includegraphics[height=0.32\textheight]{maple/l-2_m-1}
$ P_2^1(\cos\theta)=3 \sqrt {1- \left( \cos \left( \theta \right) \right) ^{4}} \left(
\cos \left( \theta \right) \right) ^{2} $
$ l=2$  
$ m=2$ \includegraphics[height=0.32\textheight]{maple/l-2_m-2}
$ P_2^2(\cos\theta)=3-3  \left( \cos \left( \theta \right) \right) ^{4}
$
$ l=3$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-3_m-0}
$ P_3^0(\cos\theta)=\left( \cos \left( \theta \right) \right) ^{6}+3/2  \left( ...
...a \right) \right) ^{4}-1 \right) \left( \cos
\left( \theta \right) \right) ^{2}$
$ l=3$  
$ m=1$ \includegraphics[height=0.32\textheight]{maple/l-3_m-1}
$ P_3^1(\cos\theta)=\sqrt {1- \left( \cos \left( \theta \right) \right) ^{4}}$ $ \left( 15/2
  \left( \cos \left( \theta \right) \right) ^{4}-3/2 \right)$
$ l=3$  
$ m=2$ \includegraphics[height=0.32\textheight]{maple/l-3_m-2}
$ P_3^2(\cos\theta)=15  \left( 1- \left( \cos \left( \theta \right) \right) ^{4}
\right) \left( \cos \left( \theta \right) \right) ^{2}$
$ l=3$  
$ m=3$ \includegraphics[height=0.32\textheight]{maple/l-3_m-3}
$ P_3^3(\cos\theta)=15  \left( 1- \left( \cos \left( \theta \right) \right) ^{4}
\right) ^{3/2}$
$ l=5$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-4_m-0}
$ P_4^0(\cos\theta)= \left( \cos \left( \theta \right) \right) ^{8}+3  \left( \...
...{4}+3/8  \left( \left( \cos \left(
\theta \right) \right) ^{4}-1 \right) ^{2} $
$ l=5$  
$ m=0$ \includegraphics[height=0.32\textheight]{maple/l-5_m-0}
$ P_5^0(\cos\theta)=\left( \cos \left( \theta \right) \right) ^{10}+5  \left( \...
...ht) \right) ^{4}-1 \right) ^{2} \left( \cos
\left( \theta \right) \right) ^{2}
$


next up previous contents index 537
Next: Radiale Wellenfunktionen, Laguerre-Polynome Up: Wellenfunktionen Previous: Wellenfunktionen  Skript:  PDF-Datei Übungen:  Blätter
Othmar Marti
Experimentelle Physik
Universiät Ulm