Benutzer:MichaelE/sandbox

Quantentheorie

s-type modes

Drum mode $u_{01}$	Drum mode $u_{02}$	Drum mode $u_{03}$
Wave function of 1s orbital (real part, 2D-cut, $r_{max}=2a_{0}$)	Wave function of 2s orbital (real part, 2D-cut, $r_{max}=10a_{0}$)	Wave function of 3s orbital (real part, 2D-cut, $r_{max}=20a_{0}$)

Komplexe Wellenfunktionen in Wasserstoffähnlichen Atomen

Orbital	Wellenfunktion des Orbitals				Form der Wellenfunktion $\Psi ({\vec {r}})$ (nicht maßstäblich)
	$n$	$l$	$m_{l}$	$\psi _{n,l,m_{l}}(r,\theta ,\phi )$
1s	1	0	0	${\frac {1}{\sqrt {\pi }}}\left({\frac {Z}{a_{0}}}\right)^{\frac {3}{2}}e^{-\textstyle {\frac {Zr}{a_{0}}}}$
3p-1/+1	3	1	±1	${\frac {1}{81{\sqrt {\pi }}}}\left({\frac {Z}{a_{0}}}\right)^{\frac {3}{2}}\left(6-{\frac {Zr}{a_{0}}}\right){\frac {Zr}{a_{0}}}e^{-\textstyle {\frac {Zr}{3a_{0}}}}\sin \theta e^{\pm i\phi }$	$m_{l}=-1$	$m_{l}=+1$