Gruppentheorie in der Physik I und II Vorlesungsskripte WS 2004
Transcrição
Gruppentheorie in der Physik I und II Vorlesungsskripte WS 2004
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(75 ' ' ' % (7 I I I ' ' ' 67 ' ' ' 67 ' ' ' ::. 4 5 + 5 3 0 3 6# $ % 7 I ' C6#@ 7 C6$@ 7 C6%@ 7' I C6'#7. 6$ 7 C6' % 7 ¼ ¼ 05 0C -G! A! - !+ ! * % . M " +0 . 6 7 ! & #D! ." ' ' :G05 # $ % 7 C6'#7 C6' % 7 ¼ 6 I ' ' ' ' ' ' ' ' ' Q ' ' CW$ 6 @ M @ 7X ' Q ' ' C6$@ 7 , C6$@ 7 C6'#7 C6' % 7 ' ' ' ' ' ' ' ' . 6$ 7. 6$ 7 ¼ I ¼ ¼ ¼ ¼ ::" . $7 6 ' ' ' ' Æ Æ .6 7 6$ 7.6 7 6$ 7 6 7 6 7 . 6$ 7. 6$ 7 I + $ I W M +6$ 7X I ¼ ¼ I +5 C ¼ $ 8 ¼ $ I + I + 0 0 8 $ 0 0 + !+ . 6$ 7 I WE C 67 ¼ E E I I 7 ::( <!& 8 $ E X ¼ 6 7 G & ! *,67 *>67 ! + 1+'!'-Æ& ! # ! 0& ! / 0 7 ::- . 6$ 7 I . 6$ 7 ¼ ¼ " 5 1+'!'-Æ& 67 6 7 4 ! $ 0+ ::, $!+!+ *; !',! % !! & *; . ¼ 5 67X I W @X I 67 I C6# @7 D 67 "! ! *; !. ' 3! *; ,! 8&"! & !' ! ! 0 6 9"!"!7 & ! 68' &"! & @( @ 7 + Æ& + <!' W C ;F D ! 9!.! ! I 0! :: * + $% 67 67 I W@ X I ! ' ' I Æ Æ ¼ D5 5 W ¼ @ X I W@( X I 6 M 7 ' ' I ' @( ' I ' @( ' I 6 M 7 ' ' W 6 M 7 6 M 7X ' ' I 6 76 M M 7 # M M . I ' ' I : Æ 5 W@ X I ' ' ' I '@ ' I ' @ ' I ' ' ' ' I ' ' ' I : !"! ' . ! 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' I I I 1'-Æ& 2"!% + !+ & ! !. * M 5 F 6Q ' 7 I ! ¼ ¼ ' ' D ' ! ¼ 6 (7 ! ,! 7 @( F 6Q '7 I 6 M 7F 6Q ' 7 @ I ' @ I 6 M 7 ' 6' 7F 6Q ' 7 6/C D & ! ' F 6Q ' 7 I Æ Æ 6 7 ¼ ¼¼ ¼ 6 47 ¼¼ ? D 6 (7 . 6 7 ¼¼ ¼¼ I F 6Q ' 7 ' D ' ' ' D ' ' D ' ! ! ¼ ¼¼ ¼¼ ¼ ¼ 6 7 I !! ! Æ Æ ' I ! ' ¼ ! ¼ ¼ ¼ ¼ *+J+ & D 0 ' ! ' ' ' F 6Q '7 ' D ' Æ Æ 6 7 ' ' D 6 7 ! ' D ' I I ¼¼ ¼¼ ¼¼ ¼¼ ¼ I ¼¼ ¼ ¼¼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Æ Æ / ( ( I 67! ! ! I W X ! -&0S5 R ( ( X I / 6 7 W :: ! 43 + ' !+ ! !! 8+'!',! ." 80 6 !+"! *7 I (' M ! 67 - ! ! 0!+ A . + ! *' I ." 80 6 L L #!& ." ! 0!+ :! ' 0 :!! 0 6 7 1' 8+ 6$ I % ! ." 6 7 I !+ I I .7 ! ( (5 ( + ( ( J ( F ( 6( 7 I 6( +7(56( +7 56 M 6( +7(5 6( +756 ( (5 I = I ( 6# :!! 0 D A " +07 & , ( ( . I ( M' ( 0+ "! ! )!D"! I M 96((7 " + >!!C ." 8 : &!' "! *" !& " D ! <!C #< ' (5 (#<' ' & ( ( I 'W (X I 'W ' M ! 67(X # <' W( (5 X#<' I 6" " 7#< '( (5 #<' = I " " 6! 8!7 + ( (5 I 67 5 ¼ ¼ ¼ ¼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Æ.. Æ. . ¼ ¼ 6 7 6 7 5 '*5 , I ( # " % 1+'!'-Æ& > 2 0 / M I I / I M / I I I 0 0 0 / ;0!+ -!"! ! !" +0 + /&"! I I I I / I 0 M / / 0 0 M I 0 / !+ ! )!!!+!0 0 I 6 7 I / M / / !! I I M M 0 σ (π+) 1 2 σ (π 0) σ (LA) # 5 +0+ ." :'?0'* 6' + /! +0+5 2D +0 &' ! "! ! 7 I I / 0$+ ! & 7 / *+D0; " ." >! !+ 6- 8+ 7 B .4 I '/ .`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"+ - 5 ; ; E E F F E E A" ! *>62 7 + ! + 9; *% G !+ 9!.! ! -5 ; F ; E E I E ; I ; F E E I E F I F * 6; 7 !. & A!!! * 6F 7 & !& 0C 0G ! I I 9 :: 8 *>62 7'9 2 '0 ,G0% ! & *>62 7 D I 6 I 7 !. ::. 600 5 63 : 2"! &!&' *; D + 2"! 90 , , , ." !; ." < & *;+5 , I E , E , E I E , E 8 D -Æ& D"! % ! 2! ! &!& *; !. & *>6 7 D , , I I I5 I 2 E , E , E E , E , E E , E , E E , E I E , E I5 E , E - %:23 2*3 / !!& !. 8 ! ! A! !"!0 B!0''+D0 6&."!7 *; B15 + *0!! % = 6 , I (( <=% ' ' % ' - ;+ !' ' I 4 <=7 A!!! *>67% *>67 # % D0 !. &D! 0C '3! a ,? 6 75 E E E E E E ? . :;0!+ + 6 7 2! 'B!0 6 'B!07 /G0 M 6 7 <!C! /!' ! + :!'<!& 8 ! B!0&! ! 8 ;I ; E ; 8 *!!C+D ; I ? ; . - !. & *>67 ! ? ? I . . *>67 *.!% ! " 75 >% ? . "!$ ! 6 I *>67 6 7 I 8 I I ! I I % !+ I *>67 # * ." ?' .'B!0 6&D 67 7% " !" + - & + #$!0 ! * 6 7 8"! F I ?[ F I .[ 9!.! ! ?[ .[ ?[ .[ 67 6 7 *>67 6H7 "!% !+ #$!0 + * & + <& !& 67 ." 8 A % [ [ [ I [ [ I [ ?. ? . . ? ? [ ? [ ? [ .[ I .[ I .[ ! ! D ! 9!.!+!. 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