Seite:Hans Euler Über die Streuung von Licht an Licht nach der Diracschen Theorie 1936.pdf/33

	Hans Heinrich Euler: Über die Streuung von Licht an Licht nach der Diracschen Theorie

${\begin{array}{ll|l|l}(8,4)&\left\{{\begin{array}{c}{\text{Nach}}\left.{\begin{array}{cc}(5,2),&(5,3)\\(2,2),&(2,6)\end{array}}\right\}{\text{ist das Matrixelement}}\\{\text{der Feldfunktionen}}:\end{array}}\right.&{\frac {1}{D}}\left(g^{1}g^{2}\left|\int ({\mathfrak {BD}})^{2}dV\right|-g^{3}-g^{4}\right)&{\frac {1}{D}}\left(g^{1}g^{2}\left|\int ({\mathfrak {B}}^{2}-{\mathfrak {D}}^{2})^{2}dV\right|-g^{3}-g^{4}\right)\\\hline (8,5)&\left\{{\begin{array}{c}{\text{gleich:}}\\{\text{Darin bedeutet}}\ D\ {\text{die Konstante}}\\D=\left({\frac {ch\hbar }{V}}\right)^{2}{\frac {1}{\hbar ^{4}}}{\frac {V}{\sqrt {g^{1}g^{2}g^{3}g^{4}}}}\end{array}}\right.&{\begin{array}{c}\sum \limits _{\textrm {Perm}}\left|{\mathfrak {e}}^{1}{\mathfrak {e}}^{2}{\mathfrak {g}}^{2}\right|\left|{\mathfrak {e}}^{3}{\mathfrak {e}}^{4}{\mathfrak {g}}^{4}\right|g^{1}g^{3}\\\\\\\end{array}}&{\begin{array}{c}\sum \limits _{\textrm {Perm}}\left({\mathfrak {e}}^{1}{\mathfrak {e}}^{2}\right)\left({\mathfrak {e}}^{3}{\mathfrak {e}}^{4}\right)g^{1}g^{2}g^{3}g^{4}\\-2\sum \limits _{\textrm {Perm}}\left({\mathfrak {e}}^{1}{\mathfrak {e}}^{2}\right)g^{1}g^{2}\left(\left[{\mathfrak {e}}^{3}{\mathfrak {g}}^{3}\right]\left[{\mathfrak {e}}^{4}{\mathfrak {g}}^{4}\right]\right)\\+\sum \limits _{\textrm {Perm}}\left(\left[{\mathfrak {e}}^{1}{\mathfrak {g}}^{1}\right]\left[{\mathfrak {e}}^{2}{\mathfrak {g}}^{2}\right]\right)\left(\left[{\mathfrak {e}}^{3}{\mathfrak {g}}^{3}\right]\left[{\mathfrak {e}}^{4}{\mathfrak {g}}^{4}\right]\right)\end{array}}\\\hline (8,5)&\left\{{\begin{array}{c}{\text{Dies wird im Fall der}}\ \bot \ Polarisationen:\\{\begin{array}{rcc}(x)&(y)&(z)\\{\mathfrak {e}}^{1}={\mathfrak {e}}^{2}=(0,&1,&0)\\{\mathfrak {e}}^{3}={\mathfrak {e}}^{4}=(0,&0,&1)\end{array}}\end{array}}\right.&{\begin{array}{cc}=2&\left[{\begin{array}{cc}2{{\mathfrak {g}}_{x}}^{1}{{\mathfrak {g}}_{x}}^{2}g^{3}g^{4}&+2{{\mathfrak {g}}_{x}}^{3}{{\mathfrak {g}}_{x}}^{4}g^{1}g^{2}\\-{{\mathfrak {g}}_{x}}^{1}{{\mathfrak {g}}_{x}}^{3}g^{2}g^{4}&-{{\mathfrak {g}}_{x}}^{1}{{\mathfrak {g}}_{x}}^{4}g^{2}g^{3}\\-{{\mathfrak {g}}_{x}}^{2}{{\mathfrak {g}}_{x}}^{3}g^{1}g^{4}&-{{\mathfrak {g}}_{x}}^{2}{{\mathfrak {g}}_{x}}^{4}g^{1}g^{3}\end{array}}\right]\end{array}}&{\begin{array}{c}{\begin{array}{c}=\sum \limits _{\textrm {Perm}}\left({\mathfrak {e}}^{1}{\mathfrak {e}}^{2}\right)\left({\mathfrak {e}}^{3}{\mathfrak {e}}^{4}\right)\\\\\\\end{array}}\left[{\begin{array}{c}\left({\mathfrak {g}}^{1}{\mathfrak {g}}^{2}\right)\left({\mathfrak {g}}^{3}{\mathfrak {g}}^{4}\right)\\-2\left({\mathfrak {g}}_{x}^{1}{\mathfrak {g}}_{x}^{3}\right)g^{3}g^{4}\\+g^{1}g^{2}g^{3}g^{4}\end{array}}\right]\end{array}}\\\hline (8,6)&\left\{{\begin{array}{c}{\text{und bei weiterer Spezialisierung}}\\{\text{auf}}\ \Vert \ {\text{und entgegengesetzte Impulse,}}\\{\text{also im}}\ Spezialfall\ {\text{(8,2a):}}\end{array}}\right.&{\begin{array}{c}\\\\=-8|{\mathfrak {g}}|4\end{array}}&{\begin{array}{c}\\\\+32|{\mathfrak {g}}|4\end{array}}\\\hline (8,6')&\left\{{\begin{array}{c}{\text{Dagegen im Fall der}}\ \Vert \ Polarisationen:\\{\begin{array}{rcc}(x)&(y)&(z)\\{\mathfrak {e}}^{1}={\mathfrak {e}}^{2}={\mathfrak {e}}^{3}={\mathfrak {e}}^{4}=(0,&1,&0)\end{array}}\end{array}}\right.&{\begin{array}{cc}\\\\=0\end{array}}&{\begin{array}{c}\\\\=\sum \limits _{\textrm {Perm}}\left[\left({\mathfrak {g}}^{1}{\mathfrak {g}}^{2}\right)\left({\mathfrak {g}}^{3}{\mathfrak {g}}^{4}\right)-2\left(g^{1}g^{2}\right)g^{3}g^{4}+g^{1}g^{2}g^{3}g^{4}\right]\end{array}}\\\hline (8,7)&\left\{{\begin{array}{c}{\text{und bei weiterer Spezialisierung}}\\{\text{auf}}\ \Vert \ {\text{und entgegengesetzte Impulse,}}\\{\text{also im}}\ Spezialfall\ {\text{(8,2b):}}\end{array}}\right.&{\begin{array}{c}\\\\=0\end{array}}&{\begin{array}{c}\\\\=64|g|4\end{array}}\end{array}}$

Empfohlene Zitierweise:
Hans Heinrich Euler: Über die Streuung von Licht an Licht nach der Diracschen Theorie. , 1936, Seite 428. Digitale Volltext-Ausgabe bei Wikisource, URL: https://de.wikisource.org/w/index.php?title=Seite:Hans_Euler_%C3%9Cber_die_Streuung_von_Licht_an_Licht_nach_der_Diracschen_Theorie_1936.pdf/33&oldid=- (Version vom 1.8.2018)