next up previous contents index 537
Weiter: Periodensystem, Elektronenkonfiguration und Spinzustšnde Oben: Wellenfunktionen Zurück: Radiale Wellenfunktionen, Laguerre-Polynome  Skript:  PDF-Datei Übungen:  Blätter

Radiale Wahrscheinlichkeitsverteilung

Die Wellenfunktionen sind nicht normiert.

Laguerre-Polynom  
$ n=1$  
$ l=0 \Rightarrow \widetilde{R}(\rho)=1$ \includegraphics[height=0.32\textheight]{maple/rq-1-0}
Laguerre-Polynom  
$ n=2$  
$ l=0\Rightarrow\widetilde{R}(\rho)=-2 \rho+4$  
$ l=1\Rightarrow\widetilde{R}(\rho)=6$ \includegraphics[height=0.32\textheight]{maple/rq-2-0}
Laguerre-Polynom  
$ n=3$  
$ l=0\Rightarrow\widetilde{R}(\rho)=3 (\rho)^{2}-18 \rho+18$  
$ l=1\Rightarrow\widetilde{R}(\rho)=-24 \rho+96$  
$ l=2\Rightarrow\widetilde{R}(\rho)=120$ \includegraphics[height=0.32\textheight]{maple/rq-3-0}
Laguerre-Polynom  
$ n=4$  
$ l=0\Rightarrow\widetilde{R}(\rho)=-4 {\rho}^{3}+48 {\rho}^{2}-144 \rho+96$  
$ l=1\Rightarrow\widetilde{R}(\rho)=60 {\rho}^{2}-600 \rho+1200$  
$ l=2\Rightarrow\widetilde{R}(\rho)=-720 \rho+4320$  
$ l=3\Rightarrow\widetilde{R}(\rho)=5040$ \includegraphics[height=0.32\textheight]{maple/rq-4-0}
Laguerre-Polynom  
$ n=5$  
$ l=0\Rightarrow\widetilde{R}(\rho)=5 {\rho}^{4}-100 {\rho}^{3}+600 {\rho}^{2}-1200 \rho+600$  
$ l=1\Rightarrow\widetilde{R}(\rho)=14400-10800 \rho+2160 {\rho}^{2}-120 {\rho}^{3}$  
$ l=2\Rightarrow\widetilde{R}(\rho)=105840-35280 \rho+2520 {\rho}^{2}$  
$ l=3\Rightarrow\widetilde{R}(\rho)=322560-40320 \rho$  
$ l=4\Rightarrow\widetilde{R}(\rho)=362880$ \includegraphics[height=0.32\textheight]{maple/rq-5-0}



Othmar Marti
Experimentelle Physik
Universiät Ulm