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2Â¥: Originally posted by sskkyy at 2015-03-15 18:55:49
d) Tr(MiMj)+Tr(MjMi)=2n\delta_ij = 2 Tr(MiMj). ËùÒÔ£¬ Tr(MiMj)=n \delta_ij.
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ÇëÎÊÕâ¸öʽ×ÓTr(MiMj)+Tr(MjMi)=2n\delta_ij ÊÇÔõôµÃ³öµÄ°¡£¿£¿£¿£¿ÏßÐÔ´úÊýÍü¹âÁ˶¼¡£¶øÇÒÎÒ¾õµÃ²»¶Ô°É£¬Èç¹ûi¡ÙjµÄ»°ÄǵȺÅÓұ߷Öĸ²»¾ÍÊÇ0ÁËÂð£¿
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d) Tr(MiMj)+Tr(MjMi)=2n\delta_ij = 2 Tr(MiMj). ËùÒÔ£¬ Tr(MiMj)=n \delta_ij.
µ±i=jʱ£¬Mi^2=I, ÒòΪMi Ϊ Hermitian matrix, Ëü¿ÉÒԶԽǻ¯ÎªDi, ËùÒÔDi^2=I. ËùÒÔDiµÄÿ¸ö¶Ô½ÇÔªËØ£¬Ò²¾ÍÊÇMiµÄÌØÕ÷ֵΪ1£¬»ò-1.
2Â¥2015-03-15 18:55:49
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3Â¥: Originally posted by Ëá½È×Ó at 2015-03-15 19:30:02
ÇëÎÊÕâ¸öʽ×ÓTr(MiMj)+Tr(MjMi)=2n\delta_ij ÊÇÔõôµÃ³öµÄ°¡£¿£¿£¿£¿ÏßÐÔ´úÊýÍü¹âÁ˶¼¡£¶øÇÒÎÒ¾õµÃ²»¶Ô°É£¬Èç¹ûi¡ÙjµÄ»°ÄǵȺÅÓұ߷Öĸ²»¾ÍÊÇ0ÁËÂð£¿...

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4Â¥2015-03-15 22:05:27
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3Â¥: Originally posted by Ëá½È×Ó at 2015-03-15 19:30:02
ÇëÎÊÕâ¸öʽ×ÓTr(MiMj)+Tr(MjMi)=2n\delta_ij ÊÇÔõôµÃ³öµÄ°¡£¿£¿£¿£¿ÏßÐÔ´úÊýÍü¹âÁ˶¼¡£¶øÇÒÎÒ¾õµÃ²»¶Ô°É£¬Èç¹ûi¡ÙjµÄ»°ÄǵȺÅÓұ߷Öĸ²»¾ÍÊÇ0ÁËÂð£¿...

Tr(A+B)=Tr(A)+Tr(B). Thus Tr(MiMj)+Tr(MjMi)= Tr(2\delta_ij I) = 2\delta_ij Tr(I) = 2n\delta_ij.
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5Â¥2015-03-16 02:05:54
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