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Next: 6.2 Winkelanteil der Wellenfunktionen Up: 6. Quantenmechanik Previous: 6. Quantenmechanik   Inhalt

6.1 Normierte Radialwellenfunktionen Rn, l(r)

n l Schale Orbital Funktion
1 0 K s R10(r) = 2 . $\displaystyle \left(\vphantom{ {Z \over a}}\right.$$\displaystyle {Z \over a}$ $\displaystyle \left.\vphantom{ {Z \over a}}\right)^{3 \over 2}_{}$exp$\displaystyle \left(\vphantom{-{Z r \over a } }\right.$ - $\displaystyle {Z r \over a}$ $\displaystyle \left.\vphantom{-{Z r \over a } }\right)$
2 0 L s R20(r) = 2 . $\displaystyle \left(\vphantom{ {Z \over 2a}}\right.$$\displaystyle {Z \over 2a}$ $\displaystyle \left.\vphantom{ {Z \over 2a}}\right)^{3 \over 2}_{}$$\displaystyle \left(\vphantom{ 1 - {Z r \over 2a}}\right.$1 - $\displaystyle {Z r \over 2a}$ $\displaystyle \left.\vphantom{ 1 - {Z r \over 2a}}\right)$exp$\displaystyle \left(\vphantom{-{Z r \over 2a } }\right.$ - $\displaystyle {Z r \over 2a}$ $\displaystyle \left.\vphantom{-{Z r \over 2a } }\right)$
2 1 L p R21(r) = $\displaystyle {1 \over \sqrt{3}}$$\displaystyle \left(\vphantom{ {Z \over 2a}}\right.$$\displaystyle {Z \over 2a}$ $\displaystyle \left.\vphantom{ {Z \over 2a}}\right)^{3 \over 2}_{}$$\displaystyle \left(\vphantom{{Z r \over a}}\right.$$\displaystyle {Z r \over a}$ $\displaystyle \left.\vphantom{{Z r \over a}}\right)$exp$\displaystyle \left(\vphantom{-{Z r \over 2a } }\right.$ - $\displaystyle {Z r \over 2a}$ $\displaystyle \left.\vphantom{-{Z r \over 2a } }\right)$
3 0 M s R30(r) = 2 . $\displaystyle \left(\vphantom{ {Z \over 3a}}\right.$$\displaystyle {Z \over 3a}$ $\displaystyle \left.\vphantom{ {Z \over 3a}}\right)^{3 \over 2}_{}$$\displaystyle \left(\vphantom{1- {{2 Z r}\over {3 a}}+ {{2 (Z r)^2}\over {27 a^2}}}\right.$1 - $\displaystyle {{2 Z r}\over {3 a}}$ + $\displaystyle {{2 (Z r)^2}\over {27 a^2}}$ $\displaystyle \left.\vphantom{1- {{2 Z r}\over {3 a}}+ {{2 (Z r)^2}\over {27 a^2}}}\right)$exp$\displaystyle \left(\vphantom{-{Z r \over 3 a } }\right.$ - $\displaystyle {Z r \over 3 a}$ $\displaystyle \left.\vphantom{-{Z r \over 3 a } }\right)$
3 1 M p R31(r) = $\displaystyle {{4 \sqrt{2}}\over 3}$$\displaystyle \left(\vphantom{ {Z \over 3a}}\right.$$\displaystyle {Z \over 3a}$ $\displaystyle \left.\vphantom{ {Z \over 3a}}\right)^{3 \over 2}_{}$$\displaystyle {{Z r}\over a}$$\displaystyle \left(\vphantom{ 1 - { Zr \over 6 a}}\right.$1 - $\displaystyle {Zr \over 6 a}$ $\displaystyle \left.\vphantom{ 1 - { Zr \over 6 a}}\right)$exp$\displaystyle \left(\vphantom{-{Z r \over 3 a } }\right.$ - $\displaystyle {Z r \over 3 a}$ $\displaystyle \left.\vphantom{-{Z r \over 3 a } }\right)$


Alexander Wagner
2000-04-14