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6.2 Winkelanteil der Wellenfunktionen (= Kugelflächenfunktionen)

l m Funktion
0 0 Y00 = $\displaystyle {1 \over {\sqrt{4\pi}}}$
1 +1 Y11 = - $\displaystyle \sqrt{{3 \over {8\pi}}}$sin($\displaystyle \theta$)ei$\scriptstyle \varphi$
1 0 Y10 = $\displaystyle \sqrt{{3 \over {4\pi}}}$cos($\displaystyle \theta$)
1 -1 Y1-1 = $\displaystyle \sqrt{{3 \over {8\pi}}}$sin($\displaystyle \theta$)e-i$\scriptstyle \varphi$
2 +2 Y22 = $\displaystyle \sqrt{{15\over{32\pi}}}$sin2($\displaystyle \theta$)e2i$\scriptstyle \varphi$
2 +1 Y21 = - $\displaystyle \sqrt{{15\over {8\pi}}}$cos($\displaystyle \theta$)sin($\displaystyle \theta$)ei$\scriptstyle \varphi$
2 0 Y20 = $\displaystyle \sqrt{{5\over{16\pi}}}$[3cos2($\displaystyle \theta$) - 1]
2 -1 Y2-1 = $\displaystyle \sqrt{{15\over {8\pi}}}$cos($\displaystyle \theta$)sin($\displaystyle \theta$)e-i$\scriptstyle \varphi$
2 -2 Y2-2 = $\displaystyle \sqrt{{15\over{32\pi}}}$sin2($\displaystyle \theta$)e-2i$\scriptstyle \varphi$
3 +3 Y33 = - $\displaystyle \sqrt{{35 \over 64 \pi}}$sin3($\displaystyle \theta$)e3i$\scriptstyle \phi$
3 +2 Y32 = $\displaystyle \sqrt{{105 \over 32 \pi}}$sin2($\displaystyle \theta$)e2i$\scriptstyle \phi$
3 +1 Y31 = - $\displaystyle \sqrt{{21 \over 64 \pi}}$sin($\displaystyle \theta$)(5cos2($\displaystyle \theta$) - 1)ei$\scriptstyle \phi$
3 0 Y30 = $\displaystyle \sqrt{{7 \over 16 \pi}}$(5cos3($\displaystyle \theta$) - 3cos($\displaystyle \theta$))
3 -1 Y3-1 = $\displaystyle \sqrt{{21 \over 64 \pi}}$sin($\displaystyle \theta$)(5cos2($\displaystyle \theta$) - 1)e-i$\scriptstyle \phi$
3 -2 Y3-2 = $\displaystyle \sqrt{{105 \over 32 \pi}}$sin2($\displaystyle \theta$)e-2i$\scriptstyle \phi$
3 -3 Y3-3 = + $\displaystyle \sqrt{{35 \over 64 \pi}}$sin3($\displaystyle \theta$)e-3i$\scriptstyle \phi$


Alexander Wagner
2000-04-14