Weiter: Periodensystem, Elektronenkonfiguration und Spinzustände Oben: Wellenfunktionen Zurück: Radiale Wellenfunktionen, Laguerre-Polynome Skript: PDF-Datei Übungen: Blätter

Radiale Wahrscheinlichkeitsverteilung

Die Wellenfunktionen sind nicht normiert.

Laguerre-Polynom

$l=0 \Rightarrow \widetilde{R}(\rho)=1$ $\includegraphics[height=0.32\textheight]{maple/rq-1-0}$

Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=-2 \rho+4$

$l=1\Rightarrow\widetilde{R}(\rho)=6$ $\includegraphics[height=0.32\textheight]{maple/rq-2-0}$

Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=3 (\rho)^{2}-18 \rho+18$

$l=1\Rightarrow\widetilde{R}(\rho)=-24 \rho+96$

$l=2\Rightarrow\widetilde{R}(\rho)=120$ $\includegraphics[height=0.32\textheight]{maple/rq-3-0}$

Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=-4 {\rho}^{3}+48 {\rho}^{2}-144 \rho+96$

$l=1\Rightarrow\widetilde{R}(\rho)=60 {\rho}^{2}-600 \rho+1200$

$l=2\Rightarrow\widetilde{R}(\rho)=-720 \rho+4320$

$l=3\Rightarrow\widetilde{R}(\rho)=5040$ $\includegraphics[height=0.32\textheight]{maple/rq-4-0}$

Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=5 {\rho}^{4}-100 {\rho}^{3}+600 {\rho}^{2}-1200 \rho+600$

$l=1\Rightarrow\widetilde{R}(\rho)=14400-10800 \rho+2160 {\rho}^{2}-120 {\rho}^{3}$

$l=2\Rightarrow\widetilde{R}(\rho)=105840-35280 \rho+2520 {\rho}^{2}$

$l=3\Rightarrow\widetilde{R}(\rho)=322560-40320 \rho$

$l=4\Rightarrow\widetilde{R}(\rho)=362880$ $\includegraphics[height=0.32\textheight]{maple/rq-5-0}$

Othmar Marti
Experimentelle Physik
Universiät Ulm

Laguerre-Polynom

$l=0 \Rightarrow \widetilde{R}(\rho)=1$	$\includegraphics[height=0.32\textheight]{maple/rq-1-0}$
Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=-2 \rho+4$
$l=1\Rightarrow\widetilde{R}(\rho)=6$	$\includegraphics[height=0.32\textheight]{maple/rq-2-0}$
Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=3 (\rho)^{2}-18 \rho+18$
$l=1\Rightarrow\widetilde{R}(\rho)=-24 \rho+96$
$l=2\Rightarrow\widetilde{R}(\rho)=120$	$\includegraphics[height=0.32\textheight]{maple/rq-3-0}$
Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=-4 {\rho}^{3}+48 {\rho}^{2}-144 \rho+96$
$l=1\Rightarrow\widetilde{R}(\rho)=60 {\rho}^{2}-600 \rho+1200$
$l=2\Rightarrow\widetilde{R}(\rho)=-720 \rho+4320$
$l=3\Rightarrow\widetilde{R}(\rho)=5040$	$\includegraphics[height=0.32\textheight]{maple/rq-4-0}$
Laguerre-Polynom

$l=0\Rightarrow\widetilde{R}(\rho)=5 {\rho}^{4}-100 {\rho}^{3}+600 {\rho}^{2}-1200 \rho+600$
$l=1\Rightarrow\widetilde{R}(\rho)=14400-10800 \rho+2160 {\rho}^{2}-120 {\rho}^{3}$
$l=2\Rightarrow\widetilde{R}(\rho)=105840-35280 \rho+2520 {\rho}^{2}$
$l=3\Rightarrow\widetilde{R}(\rho)=322560-40320 \rho$
$l=4\Rightarrow\widetilde{R}(\rho)=362880$	$\includegraphics[height=0.32\textheight]{maple/rq-5-0}$