L P LP. j j Q = 1 P =

Transcript

1 ! "!#$%# &')(*! $+ +!#$,-+! $(* " / !!+! 87 9&:(;< = QMTON J H4E/QMTOIOI WXH4TOQME/LOIZY []\ EUGOH4TOQMLKLON^ QM_MQ \ QM`KEUG abq \ E/GZc \ u -v* >ẍw, "! > " " <( $yz $+ $ 7 {&( }< = K!~-.3!.3!! ƒ ~

2 QU EUT ˆ VMLOIOE Š Œ Ž :Œ* : : *Ž " š> O nœ*ž œ; ž * - ržÿœ ~".h~ &: {"+! ( " ()+* " " * 7< $!+ UK# ""+ )+ ")+! " U! $(!( ~".3 k7< $!+ U! $(!(.M...M...M...M...M...M...M...M... ~$ ~".6 8<" >") "++ / M!+!yª $+ w 7< $!+ «?O" ()""(!..M...M... ~!~ :ž n±ž ²³ > :ž Ÿ² Œ *µ ¹ Ž º³»n ² š> K K > nœ*ž œ ž * :ž :Œ Š¼.h~ u< "(! $+ v)?" "!#$, 77!+ "#%# -* ""+ )+}..M...M...M... ~$½.3 k7< $!+ U! $(!( } "!* "¾...M...M...M...M...M...M... -~.6 8+!+ wk $!( -w!!=$ -Àª + Á...M...M...M...M...M...M...! Â Ãz K > ŒŽ œ, ž * - ržÿœä» ²³š" n > žÿ :Ž Ž œ; >»Å " " P * n > - *Æ.h~ &: {"+ U ( " ()+* Ç.M...M...M...M...M...M...M...M "#$! +w" $"( w!!= -Àz $+.z.m...m...m...m...m...m... "È.6 ÉX"(-"( Ê"v!Àª O!"* { 7< $!+ «?Ë" $()""(!Ì +"#$! $"( "+ + k? * D.M...M...M...M...M...M...M...M...M...M...M... ½.Íƒ k7< $!+ U Å# -!+ )+ f 7 &: { ( ")+ Å $("+ +!M "(-"-( Î9ÏÐ ])#Ñ + + U-Ò<#) -!+ +Ó)= $+ v! $( #Ä..M...M...M...M...M...M...¾ "

3 Ô TOEX E \KÕ LONPEDÖ/VMabEUÒVMLOIZY Øš - Ž ÚÙ1Ž Û Ü )( 7< $!+ «?" $(!(!ÞÝb &: +M =X +!!+ k?m +* (- +! )+! "!ß?-)+ ØÝ #$() Á!! $( yz $+ + ³!v-à ( )³Ê $!( b (! $+ -wß b $-(! ) $.2á + "!+ +! "!!#$(! + {r% $&: $ (! $+ -w $(!+ + «?!v")! $ $! $("&: «?K!!"" -à4àz -? á $&: w á )*- $ ( -? $&:"( Ñ "Z $(!+ +!1 ("-( 7ãÚK " " ; ( â%+ K ( " " f =! + U, $&: à4 w,,( )+ ( v â; $+ -wªïð ( $+ v"( â $+ -w &: *77 ( $+ "+ U 1 $( $ ( /Ñ + $ Ü4ä Ò9.!å< *!=w;+ k"!<( = (v U > 7+! " U U $&: + 7 ()" -!+ 7! $+ )" "= â+ " $à4àª -?> æw * { #$+!( ( " "!Z) $( " =z r)# "% )Ñ &:!+ / X# -""+ )+ 1Ýb $#Þ yz ( =$!)" Ê!#$()+ $+ -wz M ( "Àz $+ -wz )+ "# #) - ""+ *+-ã yª (" * =$ æwë " + "#$ -?f >)( )+"?1+ $ $ ( -?Ë( "" $"( "+ +!#$ (! $+ -wk $!v! $+ +, ( K * $ {* {&:")+ $"( "+ +Ñç!!= v>â &: $+ + «? " w + K ( " $!* (!" $)à4àª -?K <(*)= ( U!" Xè "v!( = ")+ $ Á ( + «? w= $.ér++ 7" +! $!( Á 77!+ k?³" $(*)!(!Ë+ $"v? &: Ì&* wá (! -!+ "#$Ë! /v!"(*f(! +!#$ $&' K! $+ &: $ + " K * $ «?K( =$!)"" ã ( {&r!) w* "v!"k >â%+ $ yª M ( {&r {!+ = $- $( $+!!+ k?k $(" *" )Ñ v" $++ $"( "++ Ñç) $v)" "+Ñç!(À!+ k?1 ¹ v>!+ )Ñê!()À; *"+ «?1 $-Ñ (!,! Þ!!#$,()= ( $yª $+ wÿã + $!v? &: 1&*wO7!( (! +* ª " "v!! " * )+ -w + -wo( { w " " * Ñ -?O 77 $-!,+ (! $+ "!* * $. ë ±ì : n "œ,œ* * í!» : >» "! Ê1 $(?>$&: Ê!v! / + «? >)+! "!?+ $ -?! $(!( " &: $* "!-à4àz -?Ë" $ îv!!+ $ +! $( +! ( " ()+* "" O "w + Ë")Ê+Ñ = U >) $ U ï < $" "+ U ï! $(!( / />!""( U &: $* -à = &')+ +! ð $&: ( " "(+* " "!+ $ +!òñó)ê ()! -* + $v")!yª!:ô()=$ $( + { + + "Ìâ; +*<"( Å àïëõ ö øªù " w + Ø * { $ 7 X "Ë á æ?>$&:+ U! $( "(.Xú<+ / á {! >) X( Ê &: ûë!={&'+ ] $+!!Ø +-"!!Ø?-)+ áë=()+ $! «& $+ +! P &: ( "(+* {! " «$! ++!!v" U )+! > Ýü ())&'- yzªm! / z ) > @ " )Ñ w * { $ 7.ýnv!" ª Þ < $" "+ U Z! $(!( -= )"ª = + -?,?-)() $( * { * { $ 7 ª!-â 7 $&: (!), -?&:"!)! +, ( "*ã* {*â%+ $ -?O (!. þ : " ÿ á nžÿ "» Ž µ>ž >Ž &* ẃ {" &: $+!f!( yz -?Ê-(*! ¹ ()+! * $ = (Ñ à4àz -?ẍwû "v)r! { ³< =!Ê? $!( "( " $+ -w n )+! "!û?-)+ û ) $ w*(+ "f $"( ". 8<( " ª!#$* :w¹+ &: $à Ú -O!+ O â; Kv! U"O = + K " $ â r)à4àª ³()=!v!()" æw,"" /, ( {&r {") w à Z!v!"+; ) " û&: )*- $ ( $ K $&:!+ / 7 $&*?>$&: b )+!"!O? Ú. ÊŽ > ÿ r» n 4 Ëµ>Ž ± ÿœf * n±*µ> :Œ ±: ²áš -n : " ÿ - Û u<( {&: )r)# > æw= +Ñ! Å " " +! K + $ +!Ì#$ $v!( )+!"!?+ )+!"!?!v $!v" U + «?Ì-+! $(* " > -?¹-(*!. ä!v" + + >â%+ K- "()v!!!)" ; ] ( + U f ( {&*Ñ! ) $+ -w " ()""(! ñ ) / *,+ v" $ "+ $ + " $( + { ( " ()+* " >, " )Ñ w + ³ ³ )w = )+ + U Ö " (!v* $ ï Ç+ Kv &: $!v"()à )"f!+ ]+ -wrôz ³! $( (! > 1 ( = â; + +!#$! $(" Z v = * ) ³ { $- $(! -?%&: " $( -Ñ +)+!."u<("v! Ê $#$<!" *+-w*à æw; ( ; "!Àª ;!+&')(+ «?z- $v!+!*ã w; )r)#)àª &* wk!#$ - yª 7" $#$, $&*?>$&*w

4 Ü. É4. ) " X&:!*.*8<+-"w?-) ª = ] #$ = ~! " ú;.024. Ü v>)( $+ >" $ Ü.324.«-v*. å r³ >)+! "!b?.41. «Ïx2X / y w yª)rò9 ~ "½ K * -± : " ÿ Û 5<- yz 4 " $#$ { >M+) () $(?-%!+ = ;ö!ö#"! $ ö%)ö õ-ù. u<( {&*r)# /K" $- %+ 7( $!)++ =! >)+, " " () "! + -. Ü!(Ì ( = +*) { $+'&ï.324.3å<!! " "Ì=Z +!#$" * { $+ + U, ) = + U ;"v" >â &: $+ -w r= Ñ + -wk K ( {&* â $+ -wÿ. ƒ

5 ( ) [ IOJMLONPERQMSOEUTOVH QMTON *,+ -02-EDGFG<IHGDKJML-93N>O-4A:P6QSRF6QTFUA:DVWL%FG<YXZV[PN0W\<Z-9PSR\;DG] PG>O- V^+_\3NP-9PGF^Q: `au-9bcr - :+FGFUHG3\;PSR%:3^:<d-feK\PGF L-5EHGF6egXX-9HRFG3 PG>4eh:A-!+_\R :+ :3 i j\ k D- -l<?>y:n5 R\P:3NFG<45mQnPo\p3\.UP-9bGq1F6eU5E3^:bS5 R3\engRF6eM:NǸrs-EHSR :3Kt: `7+_\a#\Qn3 PGFG<d\PGF- Po\T5meG:/0u5 R3^:1FT+_\;v7DGF L%F-w: `>xl%p:bfzy{gxx -9HSRFG3 P:bs}dHG3^\PSR :3^:bc<Z-feK\PGFGHGF i ~!~ ƒ S w ˆ IŠ O ŒoŽ2 O ÔŒoŽu? s _ Žu ÔĨ šk œc p WŽ2 Ô ˆM l l =Ô u Ĩ ž ŠO s O?Ž2 O u<( {&: ) â /! "<+! k +- $( à <#) -!+ )+ " H M ( yª $+ ; ")!+( +!#$<-() "+ + -wtÿ( {&: +#$ $( H ψ µ = E µ ψ µ 2X X&: ËM ( " ()+*! 4 { w*+ Z * { $ á &: ( "(+* {"Ý ;![ N o;o%s ø ö : {ø " ñó!zv! &: $ b!)"* ' O $#K( = $( + " K() "+ L P M «?K! $!(! " w + -w +, $&: ( " ()+*!%+ M { yª! ]. ô r!>" " ' O (! $ ¹ {?Ì * )Ñ ä v" U + % $&: *Ñ ψ µ +! U ( " ()+*!7" ( {& w*à )ª + $ +--àø!v")! =! "+ "#$7+)v"!(;ñó!(!#$!+!+ «?ô! $!(! { m } K (! $!(+ = * U æw L P z! )+ +)v"!( ;! ³v> = * M P = m m m=1 { m } &:ªv> = * z! $ $&:!+! ( " ()+*! ". )( z ( "!( P L P 0 L P u<( "!(+ª"(""#$!+"+! &:! + + ( 9&r ") w >ẍw ])"( $ ñ L P LP Q = 1 P = j j j: j>m Ý "; o M w øo-ö : ø#"!ô

6 ú7! / %! $!( (! $""(! { ψ µ }!-â,(! w*#$ >)à + $" M Ñç $( +! % & ( "(+! L P M P = ψ µ ψ µ µ=1 øªùo"; Gª?«z {ö <ù6g ø# *ù:ö H &: $* L P Î H = P HP S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S $#$z!v"! $+ + U =$+ $+ -w,ý + +* ñ!v { " + + /! $""( ψ µ $&: + â!z!v "" $+ + k?,= + $+ % +"#$M#) -)Ñ H ψ µ = E µ ψ µ +)= Uà æw ;; [ Gª2 <ù±" "ø /ö <ù ô«-àz K + + " %v! $!+!!v!( â $+ Ω : L P = L P ñ! -ö "ª?«²" E [ o" «omö ø / ô{ $( "$&*w Àª $ 7 & "+ U! $!( b ; *! / 7 " $""( b "w + -w Î éú / " ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ³S³S³S³S³S³S³ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ ŚŚŚŚŚŚ Ω ψ µ = ψ µ Ω = ΩP 0 0

7 8<(! <!#$* PΩ = Ω ä v"( +! ¹!v!( â $+. ä $! &:+ Ω = ΩP L P = L P : Ω ψ µ = ψ µ Ýo7";ªl«µ"%9G o;"%«µo-ö ø /r. Ω = P Ω S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S 0 0 u<(! =! {&: $+ &: * %) {&: + *;+zà4v-àì<+ àî & "+!#$% ( " (*+* " > ΩΩ ( = ;à v!-àì -+ àî "+ 7 $#$ = + Ü +!#$ + éú + -(!+ $+ Ÿ( {&: +#$ $( ΩΩ = P. Ω Ω = P. ψ µ + Ω ψ µ H Ω ψ µ = ΩE µ ψ µ E µ ψ µ ÝÇ+* H ψ µ Î H Ω ψ µ = HΩ ψ µ u<" )"-Ì "v"! $+ + U,! $""( â+%!)",! $(!( + / /Î H (! { w*# >)à '"! ; $&:!+ " ; ( " ()+*! '-(!+ $+ H Ω = Ω H ñ ")+!"!! $(!( -!) ô. X" ;¹;¹º [ ;w -ö%"; o *ùo»d *ö. PH P H z" +â% 4 $#$ { $Þ+ Ω )*- ) $ w*!+ " X! /(â $+ Å&* w H $( +?M!v"(â $+ Î H = ΩH Ω ¼ XX -9HSRFG3 PG>½b 8 \<?FGDG]R%:PGF \;P ¾ D:e6\-.ru<( " $ yz Ì +) v") $ -= " {+ / >)( )+O" $Ñ ( Z * æw - )r)# - ª $&:!+ U <! $!( áýü (! $ O * " «?Z! $!(! + $&:!+! ( " ()+*! Î ψ µ = P ψ µ "f Ω = P P.Åu<( Ê&: $*! Á!!" " -à4àz $#$1! $(!( Ω +Ì>"!+ $+! "" -Ñ +!#$! $!(, % &: {"+! á ( " ()+*! M+ $#$+ M (! * æ?>$&: Ìñ P Ω P ψ µ = P Ω ψ µ = P ψ µ ôã { z!!! / X! "+ $+ Ê"v!()=-à v> = *Ẍ L P 4! $( + 4" ()""( +! k!!+"yz $+ P Ω = P, ", " Ω = P + QΩ È

8 2X U(â; $+ &* wk < $" "+!#$,# -""+ )+ H = P PH Ω = P H Ω ( K $&r!+"! ;"v!!v"àz $+ +! 7-() "+ $+ 1Å?-&') H Ω = ΩH Ω ú =#$ $! ( $ -? "!v!( â $+ Ow* + -# î â;& (! $ -w Ì + â & (! $ (" $ / Ì! $""() = { ψ µ } + $!(!#$"+*!+ = H + $ $(! ã (! $ 1>"(!, (! $ (" $ «?¹ " $""(!. ä v" U + K &:!v"+!)"* Ú ψ µ +!(-Ñ (! >)+!#æ&'&* + ψ µ ñ N µ = ψ µ ψ µ 1/2 ô«v!)"yz 7 {&: X!"v!Àª 7#$! "!(w + 7"v w= +Kv! U", $(!! / /.: ];+ 7 #æ&' ( -w+.â%+ H ( " æw ãr ( &: > æw ( w* ) w =!v"( "!+ ( ()v" 7&(-#$ >)+! ")Ñ?-)+! $(!( Ëñó! Xô. + $ +!#$ = $+ "!+!!¹= &'. 2X= " $ }" "K $!!#$!)+ "!!#$! $(!( " ()""( Å $(! "1 " ("wâ $+ + / (*!" bñ Ω ô "( /³ â $( $! &: L.*ú =7(!+ $+ -wàÿ( {& + #$ $( - P L P Ω H Ω ψ µ = E µ Ω Ω ψ µ. X", â+ ; "" ( + ])"%)K"v!!v"Àz $+ +! 7-() "+ + +; "v"! $+ + U 7= + $+ -w H ψ µ = E µ T ψ µ $(!ªÏÐ 77!+ "#$#) -!+ +Ò H M+ "(!!+ U Ø 77 )Ñ = Ω H Ω + / ò "( ß! $(!( " T = Ω Ω ") Kv! &,+ $!(!#$"+*!+ ñó!(!#$!+!+ } <. 2X $-"( ÂÁ( $yz $+ -w¹ ""Ì (!v) $! -w)ñ " " T ô{. = ; { K" $()""( Ω ù $ 9w{øOù*õK Ω Ω = ( ¹! $(!(Ì"(! $+ Ì ì!!=!()à;) $ Å æw¹ì *ẍ?>$&:+!f<!(-ñ ( T = P ) * ( "! Ω K $(!" U 7< $!+ U # -* ""+ )+! = Ω H = H = Ω H Ω ½

9 Ý ÃÄ6ÅÆ Ç%È[É%Ê^ÅGÇ. ú = " ( ")+! "!! $( "(K ;= ) * U >)à %,! &: M Ω = ψ ν ψ ν ν=1 ( Ω = Ω = ) M ψ ν ψ ν ν=1 Ëx\P:PGF L-5EHGFGbÌgXwX -9HSRFG3NPK>pb 87\;<?FGDK]R%:PGFo\P02-1Ë DV[\;v:. Í { f " â,! $ } "v)ñ " " $+ + / "!( H +!( (!+ + U >z!v " " $+ + / 4! $!( H &:" )!!(w*à M> {)Ñ! à δ µν = ψ µ ψ ν = ψ µ Ω Ω ψ ν, "Ê Ê"(""+!( (! >)+ F!!./ ]Ê= + X Ê -?á ] ( Ë $( $ ( U >)+ -w Ω ñ Ω S = (Ω Ω ) 1 $ $ ³ùÂ)ö o ù^w {ø, fâ"²")ù NÎzõ-ø Ì;¹/öº *ùo±";ª? 9 [ ^oø; Ebø,ö =Î# ; w Ïž o ÐÑ" ö; G o9ä!gõ ö%t"ò ; :ö ô. ä (""+!( (" $ b -?Ì K57 $ &: +¹!!Àª!à L ( "v!()=$"+ w P Ó S 1/2 = (Ω Ω ) 1/2 ψ µ = ψ µ = (Ω Ω ) 1/2 ψ µ, ψ µ ψ ν = δ µν u<" )"-f ( Ë! ( $!v"(*)=!+ Ê! + &: â $+1 "(&' Êñ Ω ψ µ = Ω ψ µ ô á&: â%+ }!!" " > -à4àz ³"v!( = " ³ = $+,!)+ "!!" ()""( Î ä $! $#, (! " $( * " Ω = Ω : Ω ψ µ = Ω ψ µ Ω = Ω (Ω Ω ) 1/2 Ω Ω = P, ; " Ω = Ω +!! /")+!"!Z! $(!( =! ( +Z Z!!"" -à4àz 77 $" "+ /#) -)Ñ Ω + >ö; o *ù*õk$ "ù[«ô øªùo"; Gª?«z ö <ù6g ø *ù:ö z Õ= [>ö $ H = Ω H Ω = Ω H Ω $( -". ÃÄ6ÅÆ Ç%È[É%Ê^ÅGÇ.'ýn)= + k? -= " "( -?!+!! k?! $( +"#$ r" "v! $+ + Ñ >"#$,!)+ "!!#$%! $(!( $( ""! {, $#$, " -, $&:!+ " ³ ( " ()+*! "Î Ω Ý P Ω P = P Ω (Ω Ω ) 1/2 P = P (Ω Ω ) 1/2 P = P Ω P ÖK ^Ø où Ú u<"- â% " ", ;v)?" "!<!( ( "! < $!( ñó+*! +) $ / * " Ω = P P ô{. Ω = (Ω Ω ) 1 Ω ÖK ^Ø où Ú ú =O( $yz $+ -w ( {&: X&-Àz $Ê= &' { {&" n 7< $!+ /û# -""+ )+ Å?-Ì â%+ f ( {&r ")! 1f! &: H = Ω.Åu<"â - " H Ω = (Ω Ω ) 1 Ω H Ω z!v " " $++ / = + $+ -w %:ù ¹9 ùgïâ G o; < 7< $!+ "#z#) -"+ +- > * $ )Ñ #$7 ( % &r!)+ "! / ( v) -â; $++ "#$")+!"!#$" $(*)!( 7 ";<!( > )w* ) w à > æw Ω! $+ )!! > -à4àz + k?o "v"! $+ + «?O= + $+! $(?>. H

10 ÖK ^Ø où Ú z"â% " " (Ω Ω ) 1 = P PP ÖK ^Ø où Ú u<!â " " - " v)?>! O Z)+ "+ O!+"! /! $()""( Ø "#>;v! U"! /(â $+ b $( =M ( " $ "+ + U " ()""( 7Î Ω = P(P PP ) 1/2, Ω = P(P PP ) 1 ~ ÜÛ Ý _,Žu O?ÔĨ Þ Š _ O lžu O ø ù "; [ªl«zomö ø / Ã *!!! -à4àz )+! "!?-)+ >" O! $()""(- A &: $* ; $&:!+ " ³ ( {()+*! "Î Ã = P ÃP $#$ ] ( + / Ì $ + k! / * { $+ + U f Ì!v {! $+ + / ò" $""(* ò 77 $"!+ "#$ #) - ""+ *+- )&:) â+ "! &')"M /!!"" -à4àz, ])"( + U % * $ $+") A â;&¹ñ + "( ( "++ / :ôk "v"! $+ + U " $-!( K +"#$,#) -!+ )+ ñó - + " A µν = ψ µ A ψ ν N 1 N µ ô. µ Nν 1 A µν = ψ µ A ψ ν Ú { &* +O!v " " + + k?ì " $""(! H ; {&: -Ñ ß U w ψ ν = Ω ψ ν " (w-â $+ + "!!"+ "yz $+ ψ ν = ψ ν Ω -= ) * /) $ ψ µ A ψ ν = ψ µ Ω A Ω ψ ν = ψ µ Ã ψ ν, #æ& 7 b! ( {&: w $ 7< $!+ /K! $(!() Ã = Ω A Ω. Í { Ì!+!!"¹! $(!( ù $ 9ø :ù õg * { ψ µ } { ψ µ }!#Kv! U"O+"( (!+ + {&: -Ñ + ¹$&:+! "( $ + + *ãÿ!#æ&' ψ µ Ã ψ. u<" *"f "" {*- )!! &') Ì ν = A µν Ω!" 9&: $+ +! «! ( {&: + «7< $ "+!#$ " $(*)""(Þ ()" {&* "4 <&* wz 7< $!+!#$4# -)Ñ Ω ""+ )+ ( A = H ). 2Ê {*- ) / ( " =!)"+!% )(!+!! k?;" $(*)!(!ñ Ω, ô,+ $ $( "" /!v "" Ω H +!?-â; ".*2X)Ñç $(! k?ú H = ΩH Ω Ω H Ω, "z z 7< $!+ UZ#) -!+ +Zz+)yª " ( {&: $ $" "+"#$z" $()""(+ 4! -Ñ U >) æwÿ. 8<( " <!#$ + 7" + ; &:"v!+ * ", ] ( + /K $ $+%! $( "(* Ã = Ω A Ω Ã µν = ψ µ Ω A Ω ψ ν = ψ µ A ψ ν!"!v!àª #$!"!(wÿ ()" $+ X { Ø!v " " $+ + / "!( < $" "+!#$Ê# -!+ )+ A +!( (! >)+ b+ {&: + -fñ -= + +!( µν { ψ µ } * >"( $ 7 $#$* + {&: + + 4ô{. ~$

11 é&: $ - +! + "* n o "ª K 7;¹) {ø "% [ Gª c" ø /oª+ $ $(!! $(!( n "" ³ { K 7< $!+!#$,#) -!+ +* ψ µ : ψ µ H = ψ µ E µ, - H ψ µ = E µ ψ µ, + P!Ì!v! / + «?òñ () " «?ô + "(""#$!+"+ ü&:(#%&:(-#> + ²¹ù fø :ö [ [ªðñ Ê (! " > -à4àz $K+ "( ( "! T¹ ùofø# o/ög [ªUôX () " U! $!() / ; ψ µ ψ ν = δ µν ÖK ^Ø où Ú z"â% 7v! "(""#$!+"+ " &* w {* w E µ E ν ú7 )!=!+ Þ $ " «?!v "" $+ + «?! $!( "z = ") w ª= ) * z ()" UZ!+!!"Z! Ñ (!(K,! &: M Ω = ψ ν ν=1 ñ "( ( $+ ",!>"K= ) * (!! $(w > æwo&: $* {! $ Á+ ψ ô{.:éú / * % "! > {!àþñ µ Àz $ 7 ( {&r!) $+ = ) " %!v;+!( (!! "v" "" $+ + «?K! $!(!*Î Ω ψ ν å< $ {&* $+ +,-v! â &' $ ÅẍwŸ Ω = M ν=1 ψ ν N 2 ν ψ ν ψ µ H ψ ν = δ µν E µν = H µν. ä ( 9&: K $< $" "+ UÌ" ()""(¹ (! =!!+!¹ " +!f+!#$ f ª 77 $-Ñ " "+ U ³#) -!+ +! Ã = ΩA Ω 1 ( 9&: â% * Ÿ { ψ µ } of ù ;"!ö [ªµ :ö ùg *ù[à[áñ N ν = 1 ô{ - {* {&:"!+ * Ÿ+ "(! $!(! { ψ µ }!, {&: + b + 7 )*- ) $ Ã = µν ψ µ ψ µ Ã ψ ν ψ ν ~ âá ψ µ Ã ψ ν = ψ µ A ψ ν = A µν œœcä4ž_?åo O?ÔÔ Ì ÞŒ?Žuˆ æ _ˆ,ç = Oçè s _,Žu O?Ô 'éê Š _?Žu Ë1:<?<WVSR\ëGF:PKPG>=-d57: :RP:q #$()à -à4 $-à ( ) / >)+! "!M?-)+ ".ú = yz+ #$!!"( ",, â%+ { K " U( â $+ wk! "!( >"!("&: + b K " [x, p x ] = i - K;( ) +" $#$(" ª&:! -â; + -woýç+ <=! * æw Àª -?O%!( $ $+! $(!(! A : [A, H ] = 0 ~!~

12 Í Àª Þ ( $( Î>" $"( = ) $&: $*! * á! { Z Þ =* $+ $ Ë * *!=$" > æw" n>ñ!!+ +! "+!yz $+ [x, H ] = i m p x #æ& m Ý ] $ ª 7.2X U * { $+ 7 ])"( + «?O $ +! $!"K K (!"K "!!+Ñ yz $+ -wk â;&%&:- nw "v"! $+ + U "!( ( "$&: %K()" $+* { (E µ E ν ) ψ µ x ψ ν = i m ψ µ p x ψ ν, =K!( "#$f { {&* 1 " $++ " f ( 9&r ") + û&* + Ç ³!( " Ê&: ) wê&* ẃ - " - w!( ", (?>$&:! *. 2X= + "! ( " zz?()+ $+ >"! "+ + «?!!"+ "yz $+ ( $(? &: U -Ñ + «?¹! $(!(!f -?¹ $< $" "+ U )+"# bo= &')+ +! } $&: *"+! } ( "(+* { "!ÎŸ $ { ÝÇ!!)""(K! $(!( " A H [A, ] = A A = (*! {&*!; Z&* w "! > {!à4àª -?O 7< $!+ «?O! $(!( " "+!yz $+ Ã [Ã, ] =? P ) : ä #$()+ Å æwz)+ -= " 9*- w = " ( "#$/ ")+! "!#$/" $(!(7ñ Ω = Ω, Ω Ω = [Ã, ] = Ω (A ΩΩ ΩΩ A )Ω = Ω (A P PA )Ω. 2!v"Àz $ {*- ) ]! "!( 77!+ k?7! $(!( "Þ+ &:) â $+z!!! " Å 7< $!+ U! $(!( " ³! "!( ä &:+), $ { = Ω (A A )Ω. A! " ( < (" $""(!,! " &: $+!v! $ $+ P Ω (A P PA )Ω = Ω PA Ω Ω A PΩ = Ω (A A )Ω ñ { [, P] = 0 É] {&:! -wÿî ( =$","! â; ô{. u< ""+ )+>" > ( P &*w [ì,¹; z! $(!( A = [H, A ] = = [ H, Ã]. u<" "" "+* ( ( &*w% 77!+ k?;! $(!( "!"(!&: +, " < " U +wñ > æwk() " $+! [ x, H] = i m p x 2Áªâ; < "( $ w )w = )+ + «? " w + )K (! - [ x, p x ] i û+ &:! {"+ «")ØØ " $-"(! -?Ø " w + ò+ w w*à >ẍwß!v {! $+ + / " $-"(* K+ x + p x. ~

13 ñ ÍÅ { Ý +" $#$( &:! -â; $+ wìñ " $(!( Å" n (-à Àª Á H ô H "v!à w $ ]!v " " $++ $""(!.^ z! > " / > "( " + ") "; ( + &*Ñ L â,àz 7 " w*+ w+ < " U( â;&: $+ } 7 " w + -w* O = $#,!(!#$!+!+!#$ª&:" ) Ñ P + $+ -w L P Î E µ E γ µ : ψ µ L P γ : ψ γ L P "#æ&rû ( ß $(?>$&: ¹!ûà4v!"#$ +v!"(* "v"! $+ + «?ß! $!(! H "v"! $+ + «?Ø! $!(! ß+v!!(Ø"v!Àª? H $&: ( " ()+*! + = + > æw. ä à«&'ë ( =$ L { {& P >" > ( P &* woà4v!!#$,! $( "(* A. = [, A ] = = [, Ã] n "v!( = " / ( $(?>$&: 7< $!+ "Ò +""!"?+ > z % $&:!+! á ( )Ñ "(+* {! Z?()+-w* æwf yz!!!+ «?Ë!!"+ "yz $+ Ÿ$&:+> ( Ë+ $>!!( «? &:! )+!+ «?O> {!! -w?o + #$( * ò&:! -â $+ -w?()+-w à!" / {. í FG<?<Z-R +F6QTgXwX -9HSRFG3NPG>ZeU:A-!+s\R :+ :3*."ú =k-! nw + «?! Uyª k " U(â; $+ z&* w; ")+! " «?! $(!( " Ω = P(P PP ) 1/2, Ω = P(P PP ) 1 { 9& Å 1! $() -wø ( îñ -+ ")( +wá! $() -w O Å" > (-à À;wá H " ( Z Ì ô/ ( > {! " Ú r Z $&:!+ " ª ( " ()+* + )( +"+ / ô! nñ Ω Ω + " {"+ z ( "( Ìñ [O, P ] = 0 ô{ã>m! Ê {*- ) [O, P] = 0 + < &'! {> æw! / )+ ;> {*"! -w,+ $+ $! k?k (! $ -w-?k * >" «?!v " " + + k?k! $!(! Ý + M + $&:!+! ( " (*+* " ". H u > " H = ) " + ( $( U "+ U "v!( = " ³!,+ $!( "#$, )( ( q H (q) = H (0) + Dq +..., D = H q. 2X Uv! $( $ Ç $&:!+! f ( " (*+* " " w ø ö9-öøo-öi o $ ö " ù: EGº.Uå< { â%+ ")+! " "* ";&* w 77 $"!+ "#$# -!+ )+, $#$ "v"! $+ + «?! (*! {&*! "( $ Ó! ]+ÁG z $ + ])+; ;" &: E µ q = ψ µ H ψ µ = ψ µ H q q ψ µ ψ µ H q ψ ν = (E µ E ν ) ψ µ q ψ ν ÖK ^Ø où Ú u<"- â% 7 ( $&: *7< $( $+ (! %!!"+ "yz $+ -w, )() (. ψ µ H ψ ν = E µ δ µν ~$ ψ µ ψ ν = δ µν

14 $+"wz )+! >wz?+ -M $&:!+! Ê ( " ()+* " " v" «r7v" Á?> â,7+7 >)+)Ñ -àî?+ O ;#$ -!v" (! "! ( {()+*! " { H q = D n)¹ 1 ^î ä & +Ë =% (" 1 >â+ «?Ë! $! ""#$ "! ( " -Î $&: 1 $-(!+ + " "(-"(! "Ê" ( {&: w à > æwø ( v) -â $+ + / P 7< $!+ / # - ""+ *+! /.U â+ * â $ / " ( {&:," " $+",()?O!!K &: { ) (! =Ñ!$&:+-àî#) -!+ +*; ; "+ yª+ )àî ä #$()+ Å æw1 { - ß = " ( -?¹!+"! k?ì! $(!( "O ¹ $( ""! «?Ì < $" Ñ + «?O#) -!+ +".!#æ&' ß U w(!+ $+ n? )*- ) $ z *7< $( $+ (wk> 9"! 7 =! ( H q = Ω q H Ω + Ω H q Ω + Ω H Ω q. H Ω = Ω H! (wâ $+ +! M $ K!!"+ "yz $+ Ω H = H q = Ω q Ω H + D Ω + HΩ q Ω Ω = P H [ q = D + > {")+ ) $ / " Ω Ω Ω = Ω q q H, Ω Ω ] q " " ( " =$ "$&:+w 7< $!+ "#Z# -* ""+ )+;Ýï+ z " " $ Á;â; " - 7< $!+ U! $(!( (" =!$&:+ "# -!+ )+.^ wk ])"( + «?K * $ $+! ψ µ H q ψ ν = ψ µ D ψ ν + (E µ E ν ) ψ µ Ω Ω q ψ ν ï7 + Ú "± ùö õkø# ms7 *ù6 $ :ö)õk *ùg«ê ( O O! ; )v" k._ $!( -wf!= >Ñ Àz $+! = U >) % O&*w + {&: *#$!+"+ «? $ $+"" ñ $(?>$&:+ «?K= + $+ :ôu *!v" U +, ]" -Àz! $+ +. HΩ ~ƒ

15 4 - H : " ðzñònó ô óoõnö6 6ö^ó ø ù M úeû ü%ýþÿnümû_ÿ [ü ;þÿü ýÿ ýþ ÿ L P = span{ m } P = m m m Ω = PΩP Ω = P ΩP ^þü^þ ÿnÿ 6ÿ M 7ÿ 7ü%þþ7ü ÿgýÿ H L P = span{ ψ µ } P = µ ψ µ ψ µ!#"$" ÿkýû#5 6 û718 6ÿ 9 Ω = P P = P + QΩ P H = P H Ω HΩ = Ω HΩ ψ µ = P ψ µ M Ω = ψ ν ψ ν ν=1 = P(P PP ) 1 Ω = M ν=1 Ω Ω = P ü %;þ&(')û*+, ÿkþ þ Ω Ω = P ÿ.pü%þþÿnü0/ý;þ;ü;þ ü213 6ÿ ψ ν N 2 ν ψ ν H = P HP = ΩH Ω H ψ µ = E µ ψ µ ψ µ = Ω ψ µ H Ω = Ω (Ω Ω ) 1/2 ψ µ = E µ H Ω = Ω H ψ µ þÿgþ ü5 ÿkýû;5 6 û<9 Ω = Ω ( Ω Ω = P ) H = Ω H Ω Ω P = P Ω ψ µ ψ ν = ψ µ ψ ν M Ω = ψ ν ψ ν ν=1 = P(P PP ) 1/2 M Ω = ψ ν ψ ν ν=1!#"0" ü %þ<mÿ ü%ý ÿký Ã 7ü %6þ A 95xÿ ýü [ü Kü%þ+ Ã = Ω A Ω ψ µ A ψ ν = ψ µ Ã ψ ν þü= 7ÿ ÿ ýü Gü Kü%þ ü%û H A ü5 MÿKþUþü ýû* ÿ Ã = ΩA Ω ψ µ A ψ ν = ψ µ Ã ψ ν ü'>3d 7ÿ'E F /ü ÿ ýü Gü Kü%þ ü%û H "$" ý IEÿGûlû/ J K ü %;þnÿ ü%ý ÿkýÿ9 = [A, ] = = [Ã, ]AKü5 A = H + = H A + LM^þ ;ü'eý5 (N,ü%þ+ ~

16 L O ^û?û ü ý9kÿ ü%ýj ^û?û_ü ý O, [O, H ] = 0 [O, P ] = 0 = [O, Ω] = 0, [O, H] = 0 H = H (q)a q L ýû ü ýa L P þü$6+ 1ÿ q H q ÿ ASþÿcþü= 7ÿ ü%û H q ~$

17 P Q QMTOabV \KÕ LKV7Y H4EUQMTKIZY JQ7Ö/aòcIR \ Y [ QMSOEUTKVH4QMTOQMJ Ë 3^\PSR :3^:<Z-fe6\;PKF L-5EHG\QÌR%- :7+F^QÀ3^:;v7<WVGaU-9PGFGb A R\3ND6Q-RT57: Ǹ:b Po\;F` :D- -nr +_\ k 0sFGëGF:PGPG>pbSts:NRP:N5EFSR -9DK]NP:1A+ :N5 R :bfc3hr :.T- 3+_-9<uQU02:N5 R\R :^L%P: V[PGFG3^-!+W5\DG] PG>pb <Z-R :/0zA+F`DKF6.-9PGPo:8;:n3 >xl;fs5ed-9pgf6q FÀ\Po\;DGFGv\M3^:DGP:3 >4ecF gxx -9HSRFG3 PG>Zē :A-!+_\%k R :+ :3[i<T gr%:b 8 Do\;3^-<?> +_\575E<Z:R +FG< :N`anFo-A+FGPGëGFGAG>êAo:5 R + :N-9PKF6Q +KQN02:3²5 R\%k ëgf:p \ +P:bIR%- :7+oFGF 36:v7<WV[a -9PGFGbh0sD6QzgRF^e : `rs-9hsr :3 USA+FG<Z-9PGFG<Z:N5 R]hAo:DVWL\N-9<?>Ze + - vevndg]r\r :3 P- `V02- R,:89+_\PGF L%FG3\R]K5mQnv\ 0W\L\<?F#:AGFS5\PGF6QU57R+ : -9PGF6QngD-9HSR+ :PGPG>Ze :N` :D:6L-9Hc<Z:D-9HVND i ä ( {&: Á( = v! $+ #) -!+ +*, * " $ }+ o "% $ =º [ Gª?«z {ö <ù^ [ ø# *ù:ö '"% $ Nº *ùo V H = H 0 + V!!v"(*)=! / *!v" }( $yz $+ -w= &' +; "v"! $+ + U = + $+ -wo&* w = &' :ô H 0 H 0 ñó+ $!!=$ -Àª + + " H 0 k = e k k â+êv" «Êv" )*- "ûv! = ( &'-.ku<( v! &:" + "!+ * «""v! $&:!+ " ( )Ñ "(+* {!,v" «, + )( +"+ / + " " "+ ª&: $* { " w H 0 Î H 0 P = P H 0, + U {")!v" (! w*#$ > % $&:+)v"!(! Á!v " " $+ + «?O" $""(!. L P H 8<( " ;!#$ Ú ( +-wk#$! "!( "* Ú O"= -Àz $+ 0 V + M { yz! Áv!)"yz /ã*! ( {&: " Z / {WV=X8Y Z\[Y Z]Ýï+ M " (! &:) â+ Kv! U"KK+ $>!!(! } / {, $!( "= -Àz $+ K+ 7 * $ 9 {&:! >) % $ æ? &: " " Ý =)"(&:+!+ *. ] &: $ Ë>"+* "(- (! > M 77 $-!+ / Þ" ()""( ÁM $&:!+! Ë ( "(+! M" >&: ( =Ñ â $+ K % " $ $+-w V Î (0) H = H ( + <=! * % V ) + H (1) ( + $ + ;= ) " %! V ) + H (2) ( > &:( $+K V ) +... ]^?_ Ã = Ã(0) + Ã(1) + Ã(2) +... ] &:"v!+ ª&: r, " ( {&r { "! " (! $+ -w(w&' ` Ω = Ω (0) + Ω (1) + Ω (2) +... ª o1¹^; [ª ø,ö øm f oe [õ-ù øm 1-ö $ ÏÞ *ù6à o ) ms7) {ø " [ o#76 ψ µ E µ abaca ~È

18 Û½!~ ŒoŽu O sô fel _éd Œ 4 šo s _ Žu Ô?šo š6 œc, = WŽu ˆ O ˆ ä ( ( " «v?>!"!,7!( (!"! $!( ;+) v") $ U ( "."2XÑç ( " «?Ú!"!v!Àª + K $#$,+ 7= )! * ñ, ( ", (! $!( P â $+.*2X U-à4 w"= -Àz $+ " * ( =$Z= " / ô«+) "! æwo yª,+) K()=)Ñ QΩ P Ω (0) = P, QΩ (0) P = 0 g ""v! b+) K" "!+ / 7 - $+ b(w&'- "=! $ ³-()!+ $+ 1Å*? H Ω = Ω H Ω ñóv&: %+>â%+ª)">, $#$; ( " -w { $;+* "+ yª+ $ 7 $&: ( " ()+* " ">ô P Ω P $&r ")" " &'ª()=$v" $+ #) -" $!= -Àz $+ +-àî! ", K!!= Àª $+! (! {&: $ ³-()!+ $+ K! & ñó! /(â; + " - + $ +! K+ <= )" æw*àz $ Ω V ôih ñó! /(â; + M, {r)#) $ / " $ $+ K+ 7+ -â $("! V ô{ $&r ")" Ì ( {&r ")) $+ <! &: k(w&'4 ª!"( $v!" $ /!v" û()" +*!<" U +w" Ω! &:!+ ª&* w- â &:" $ $+ V ñ " + b()= + «?K $ $+ + =! * ô. V ú!.6ß $ / QH 0 Ω + QV Ω = QΩ H 0 Ω + QΩ V Ω QΩ H 0 Ω = QΩ P H 0 Ω = QΩ H 0 P Ω = QΩ H 0 P = QΩ H 0!v! $( $ + $&: $(â,)àª + $ + U Ω {r)#) $ / 7 "! Î Q[Ω, H 0 ] = QV Ω QΩ V Ω j - v:dg] 36-EPSR\.:ý )v"",+ $ ( {&r! $+ + Z <(!+ $+ $ / $&: $(â,àz Á>"! "(K+ $ =Ñ! +!#$;! $( "(* +! Z+?" æw.*ý = ( â $ " n"!(o+ª (! $ K+ª &: "+ /! $!( b $&:!+!#$% ( " "(+* " >-Î éú / " ª" ()""( Q[Ω, H 0 ] = Q[Ω, H 0 ]P = Q[Ω, H 0 ] m m. Q[Ω, H 0 ] m = QΩ H 0 m QH 0 Ω m = Q(e m H 0 )Ω m, L P m LP Q(e m H 0 ) = Q(e m H 0 )Q = j (e m e j ) j ~$½ j

19 !v"(*) b!(!#$!+!+! ò&:! *+ $+ 1f $&:!+! Ì ( "(+ > Ú { ¹)"> ä ( 9&: Á $(! $()""(Ò $ E [ " ømª e m e j. ˆ G : L P G(A ˆ ) = (Q(e m H 0 )Q) 1 A m m m L P L P = m j j j A m m e m e j ˆ GQ[Ω, H 0 ] = QΩ < $#$; "!Àz"àî = v) " Åẍw%!!)""(-Î w {r)#) $ k?o!(w-&:- n Ω (n) QΩ = ˆ G (V Ω Ω V Ω ) ( = G ˆ V Ω (n 1) n 1 ;! {+ " ;+ = yª?o "("w-&:?o - k=1 ) Ω (k) V Ω (n 1 k) ; Ω (1) = G(V ˆ L P Q ) = V m m m e m H 0 Ω (2) = G ˆ ( V G(V ˆ ) G(V ˆ )V ) = L P m Q e m H 0 V L P m,m Q e m H 0 V m m Q (e m H 0 )(e m H 0 ) V m m V m m. ñx~ô 2X $( + $ ÅẍwK 77 $-!+ -!+ )+'Î H = P H Ω = P H 0 Ω + P V Ω = P H 0 P Ω + P V (P + Q)Ω ér+ wk( =â $+ Ω ;(w& * ( & = P H 0 P + P V P + P V QΩ H (0) = P H 0 P H (1) = P V P H (2) = P V Ω (1) = P V G(V ˆ ) H (n) = P V Ω (n 1) ÉÁ- "" ³ " { {&:+ $#$, " U(â; $+ -wk â%+, $( * )"<!( *%&* w Ω (n) ( = G ˆ V Ω (n 1) n 1 ~ k=1 Ω (k) ) H (n k) Ω (n)î

20 ä $! &:+ &< $( "!#$<!(w&:þ $!( ª "= -Àz $+!-à4 {"+ H "! æw $( ""! / / $&:+),! () "!(!#$, "("w-&: H (2) = P V L P m Q e m H 0 V m m >â 7+ $(! >zý " U(â; $+ &* wk ])"( + "#% $+" m H (2) m = m L V QV m P m V j j V m = e m H 0 j e m e j w "+ ;+ ( +,!"+ "!+, $(!+!" +>&: $-! m m ÖK ^Ø où Ú u<"- â% " "Ì &:" #Z"?1-(!"+ û $+ $( # û+ $!!= n-àª $++ "#$ #) -!+ +. +ª= &')+ +-àî " w*+ +àî " + e k e k = e k + c, H 0 H 0 = H 0 + c + 7 = $+-w %( =$"!,( "ª ;" $"( K!!= n-àª $+. k- :7+F6Q13^:;v7<WVGaU-9PGFGb ¼ AGqUR -9bGPo\mlon1-57`FSR\Ki u<( {&r {") " # ""+ )+ª ] ( $ªÞ= &')+-Ñ +! }v> = * ñ H kl = ψ k H ψ ô< 1" ( {&: + $!!=$ -Àª + + /Ë#) -!+ )+!v"! $+ + / l! $!( î!( = * + U Ì! $""() Ú "! > "!-à Àª z+ $"= -Àz $+ + U ª $+ $(-Ñ #$!" *& & #$!+"+ U ])"( + / $ $+-") #) -!+ )+ñ ô -; H kk H 0 = k k H kk k e k = ψ k H ψ k ( < "= -Àz $+ -w,ý ] ( 7# -""+ )+Ü &' $++ ";& #$!+"àz.6íå 9 ( M &: z + "#$! $"( "++ "Z= &' = * 4!v"( =! >)+O { $ $(" " & $( +)+! >")!Z >Ñ ( )+ $!(!= -Àz $+ + = / > 7fùo«" $ º *ù[«[ªø «G :öqp0r1$ 7¹ù*ø;ö.!2f! {* 4 Å)( Ø - $+! ª( = â; + 7< $!+!#$ª#) -!+ +*M Z!+!!"#$ª! $( "(* ( H (0) ) mm = δ mm H mm (Ω (0) ) mm = δ mm ( H (1) ) mm = (1 δ mm )H mm (Ω (1) ) jm = ( H (2) ) mm = H jm H m m H jj LP H mj H jm H m m H jj ÖK ^Ø où Ú 2X U yª ", " U(â; $+ ª&* wf " ()! f(! $"( 1!= -Àz $+ X yz" $ +xázå< v" -" K 7< -!+ +. j ÖK ^Ø où Ú u > "%+ $!= -Àz $+ + / 7-( "!+ $+ $( #$ % $&:!+! Á ( " ()+*! M" U( â;&: {Ñ + 7Î.57 $#$Mv" {&: "ẍwÿ > " e 1 = e 2 =... = e H (0 2) M H (0) + H (1) + H (2)z! û 9*- ) $( "".2á)!!(w&: 7 ( w*! >ẍw+ $ $(!"", 77!+ "#$,# -""+ )+Nî

21 Û½ÜÛ Ý _,Žu O?ÔĨ Þ Š _ O lžu O Œ OŒŽ2 ÍÅ { K ß" ( {&: 77!+ /K! $(!() ",( = â $+ Ã Ã = Ω A Ω, ;(w& $!( K "= -Àz $+ )*- æw =( = â; $+ -w Ω Î Ã = (P + Ω (1) + Ω (2) +...)A (P + Ω (1) + Ω (2) +...) = Ã(0) Ã (0) + Ã(1) = P A P + Ã(2) +..., #æ&: Ã (1) = Ω (1) A P + P A Ω (1) Ã (2) = Ω (1) A Ω (1) + Ω (2) A P + P A Ω (2). ÖK ^Ø où Ú éú) yª " Ì! U( â $+ &*wò " ()! ò $(!"#$û!(w-&:-ë" $!( ò!= -Àz $+ X yz" $ +xázå< v" -" K 7< $()""(%&: )"+"#$, " $+-"-. Ü $( +!+!! ( {&: $+ M $< $" "+!#$,! $( "(*ñ Ã = Ω ô«( {&: :#) A Ω! / { $+ ( {&:+ -?Z= + $+ * =! >)+ $ ³v"!(!#$!+!+ «?O " $""(!. å!+&:)ñ v! > æwk( = â; + Ω,(w&. 2«! + < #-( (! >)!yª $, ( {&: «&Àª $f# r) " %!+!yª $+ Ω Ú = (Ω Ω ) 1 Ω &:) â+ ò yª;!+ ])"!+ { 9&: ;= ª "("w-&:) ñ &* w n 1 " Ω!(w&:"ô (n) P = P Ω (n) V Î Ω Ω = P + Ω (1) Ω (1) +... = 0 f! /(â $+ Ÿ *! "+ " Ÿ+ 9r# $ «?f $( "!#$ (Ω Ω ) 1 = P Ω (1) Ω (1) +... ñ =&:, ß "" yz)"+!7!( (1 x) 1 = 1 x +... ô Ω = (Ω Ω ) 1 Ω = P + Ω (1) + Ω (2) Ω (1) Ω (1) +... ÖK ^Ø où Ú 2X U " {&: " ð" U(â; $+ ð!(!#$¾ "(w&: $!(!= -Àz $+ &* w Ã =. Ω A Ω é ) / * %, $(!! Á!(w-&:> " $"(!!=$ -Àª + 7< $!+ /! $(!( *! ( {&: Ñ $++ / 4&:- nw( = + U " "v)! " *&')à. ÖK ^Ø où Ú å< / * ¹,! " $( yz $+ + +!"!," $"( %!!=$ -Àª + &* w H " $&r!! ( = â; $+ -w Ω %<!( Ω H = Ω î (H 0 + V )Ω ñ "ô -~

22 ô Û½âá ˆ ts Œ ½ uçêžu s O pçê *u_œòäiv sô O u<" (! $+ Þ" $"(!= -Àz $+ M( -?%-+!+ "#$ª<"( Å = ]4&: 484*>)= z / =!!Ñ ( $ Ì!)+ "! /! $()""(! = + " "+< {â%+ $ "Î)( $ - ( $-( ( $+"+ / k!!"+ "yz Ñ + -wo&* w " (*!"!)+ "!!! $()""(1ñ ;!+ + z!#$()+ àþ> æw)!v)"! KK 7< -!+ <&r æwÿ. QΩa ß (!+ $+ $yª+ #$Ò7v)!;!+"!"#! $(!(ñ QΩ ô«)*- ) >ẍw, ( +!Ìâ " )1 fv?>! "!Ë7!( (! "!._ßn&:"v!+ "! " 1" ()""( Ô Ẅ øªùo" o; " $ ö)ùfw w; «: ø#")ù^ Ṽ H P H 0 P = H (1) + H (2) +..., ""#æ&'þ =k!v"!v!àª $+ +"#$4-() "+ $+ -w Å?- Ω H ]-! = H Ω H )*- = P H 0 P +Ṽ Q[Ω, H 0 ] = QV Ω QΩ Ṽ, ", (!!Àª K( = )! " $+" } ( "v!()= >ẍw 2Á= &')+ +!!(w-&:> V +? &: QΩ (n) QΩ = ˆ G(V Ω QΩ Ṽ). ( = G ˆ V Ω (n 1) n 1 l=1 QΩ (l) ) (n l) H ñ w + - (n) H = Ṽ (! (n) n = 0 ô{ *" { 6±o) {øo; *ù6 QΩ ÏÂ *ù6 ù (n) Ω H w nofko öu"; %Gì/õù*ø [. (n 1) å< $ {&* $+ +,> {")+ ) $ U * ",; $(!" ³ "(w&: [NÏž [ªØõNo [ªI-ö $ w QΩ (1) = ˆ G(V ) = QΩ (1) *1:A+s\;3 HGFH P Ω â+ ;+- K = {! " -wk = " ( Î w {r)#) $ &'+ +! " $ $+ Ω Ω = P V ñó! /yz 7+ $!" #æ&: 7 " 7 ( " Î Ω (0) = P ô - u<" )"- n l=0 Ω (l) Ω (n l) = 0 Ω (0) Ω (n) + Ω (n) Ω (0) n 1 = Ω (l) Ω (n l) Ω (0) = P! $(!( P Ω $( "" l=1 P Ω (n) = 1 n 1 Ω (l) Ω (n l), 2 l=1!

23 "< {Mo -ö " ö [ì ¹; OofKo ö ªõö! {ø ùh" E[ o" ; omö ø /öîw«: {ø "ìpº «Ò"O;; [ N o9 ø ö : ø#" 9Îd";ªöÏ ö {ø, f õg $ o%ö%"; ùà *ù Ω $ ªùK ofko ^;"). 2 {* n = 1 - ]¹ "Ì ] {* {&:"!+ * Åf $( "!!(w-&:> K $!( P Ω (1) = 0!!=$ -Àª +!! &')à. Ω Ω $( +)&: $!!"+ "yz $+ Þ&* - $+! ( = â; $+ wo 77!+ "#! $()""(*.u<(! $-Ñ " (!wk!v"!v"àz $+ +! 7-()!+ $+ 1Å?-ª+ $&:!+! ( " ()+*!* +?>$&: Í { - $( ""! " = ) yz > æwk) P [Ω, H 0 ] = P V Ω P Ω Ṽ V Ṽ P Ω :Z()! $+*!* r $( -"!O! (w-â; $+ +! ª { 9&:+ $ P [H 0, Ω ] = Ω V P ṼΩ P ÉX-r &: / $ ³ Z&:ª-()!+ $+ -w ã*!!)""( ß ( K! ³!= ) + ;-+ "â,)à > æw Î P V Ω + Ω V P P Ω Ṽ ṼΩ P = 0 wo= &'+ +"#$, "("w-&:ª V - "" ³ " <!#$ â!!+"yz $+ -w Ω (0) = P $ $ P V Ω (n 1) + Ω (n 1) V P n 1 l=1 ( (l) (n l) (l) P Ω H + H &' { {& %+ 9&:!à À;w( $( ( $++w7!( rî Ω (n l) P ) 2 H (n) = 0, ä $! &:+ H (n) = 1 { P V Ω (n 1) 2 H (1) = P V P + Ω (n 1) V P n 1 l=1 ( (l) (n l) (l) P Ω H + H Ω (n l) P )} ã&* w! () "!""(!#$,!(w-&:-; ( â%+ ;= * H (2) = 1 { (1) P V Ω + Ω (1) V P } = 1 { P V G(V ˆ ) + G(V ˆ ) V P } 2 2 = 1 (2) (2) ( H + H ) 2 ÖK ^Ø où Ú 2] /! {&:," U( â $+ -wì&* w â $+ + " :ô.â%+ ;* * ) ( H (3) (3) + H )/2 ô/î H (3) (3) ñó " ( $v + $!(!Ë!! $(-Ñ H ÏÐ+ -"! $+ +! ( = $Ò ñ, " Ω (2) u<( "!! " (! $+ -wû 77!+ k?ë! $(!(! ¹!"* { Ê(v! + Ê ()? )+!+!#$O<"( ] = ]! $+* &:+ "!+* "(- (! >)+ -wì(w-&:!z" $!( Ì!=Ñ -Àz $+ &* w Ω H.]u<)*- $+ + U 1 ( {& «&-Àz $ ü()={&: <!( * Ç&* w Ã = Ω A Ω! )+ ()! {*- * ()!" P Ω (n), n 2. Ã H (3) Ýï)"Z+ z+ &:Z=v! + $+ $ " «? )Ñ

24 4 x z ðzñònó ô óoõnö6 6ö^ó ø ù H = H 0 + V H 0 k = e k k ü67ÿ 7ü%þ ˆ G 9 = Ω = Ω (0) + Ω (1) + Ω (2) +... H = H (0) + H (1) + H (2) +... Ã = Ã(0) + Ã(1) + Ã(2) +... Ω (n), H (n), Ã(n) V n L P L P L G(A ˆ ) = (Q(e m H 0 )Q) 1 P A m m = ÿgýû;5 6 ûy13 Kÿ59 m ˆ GQ[Ω, H 0 ] = QΩ m j j j A m m e m e j Ω (0) = P ÿ Sþÿ ÿ ÿ ü%ý ÿký Ω (n) Ω (1) = G(V ˆ L P ) = m Ω (2) Q e m H 0 V m m = G ˆ ( V G(V ˆ ) G(V ˆ )V )... ( = G ˆ V Ω (n 1) n 1 k=1 ) Ω (k) V Ω (n 1 k)!#"0" ü ;þ< ')û*+, ÿkþ þ H (0) H (n) H (1) = P H 0 P = P V P... = P V Ω (n 1)!#"0" ü ;þ< ÿ ü%ý ÿký Ã = Ω A Ω : Ã (0) = P A P Ã (1) = P (A Ω (1) + Ω (1) A )P Ã (2) = P (A Ω (2) + Ω (1) A Ω (1) + Ω (2) A )P... Ã = Ω A Ω : Ã(0) Ã(1) ;ütn,ü A Ã (2) = P (A Ω (2) + Ω (1) A Ω (1) + Ω (2) A Ω (1) Ω (1) A )P )ƒ

25 : þÿkþ%ü5 5{ ü7ÿgý+ ÿ 6%û/.pü%þ% 9Sýü?/^ýýü%þ þwüq 7ÿ ÿ þÿ }pü%þ+ QΩ (n) H (n) = 1 { P V Ω (n 1) 2 ( = G ˆ V Ω (n 1) n 1 l=1 l=1 QΩ (l) P Ω (n) = 1 n 1 Ω (l) Ω (n l), 2 + Ω (n 1) V P n 1 l=1 ) (n l) H ( (l) (n l) (l) P Ω H + H Ω (n l) P )} Ω (1) = P = G(V ˆ ) = QΩ (1)... Ω (0) H (0) (1) H + = H 0 A H (2) = ( H (2)... = P V P (2) H )/2!

26 ~ \ Y \ \ IOJMLONPEìQMSOEUTKVH4QMTON []\ ÌWXIKWXH4E/a abq j D6QhPo\5½A R\3ND6QGJxRFGPSR%-!+ -5?0s3\M\5EA-9HR\xA+FGD:.T-9PGFGbÀR%- :7+FKFcgXwX -9HSRFG3NPG>Ze :A- +_\R%:7+ :3UHv\0W\L\< :AGFS5\PGF6QÀgD-9HSR+ :PGP:8;:U5 R+ : -9PGF6Q<Z:Do-9HVD 3 >xl;fs5edgfsr -9DG] PG>½bz\5EA-9HSRK A:N5 R+ : -9PGF- gxwx -9HSRFG3NPG>Zē :A-!+_\R :+ :3UHG\HA+ :;k <Z-f.nVsR :^L%PG>½b gr\;ac+_\5l-r\#ek\7+_\hsr -!+FS57RFGH g D-9HSR+ :PGPG>ZeÌ57:N5 R : Q[PGFGb F A-!+ - k ek:f02:3 F PG>ZeÀ:N` :D:6L-9Hc<Z:Do-9HVND i R%- :7+F^Q'gXwX -9HSRFG3NPG>Ze :A-!+_\R%:7+ :3ÒHK\;H':N5EP:3\U<Z:f0W-9D-9bI5 R+_:N-9PGF6Q gdo-9hsr+ :P k áp!~ ƒ S w ˆ Ĩ ÞŠO ŒoŽu O?ˆ=ŒoŽu å v!* $ ª"v! / + /Ì "!vz "( " $+ -wì $&:!+ k? ( " ()+*,&* w ( -*â $+ "v)ñ r )+ = $(!+ +! ("-( ß * $ "! % % { {&*-à4àª /Î 7!( (" $ ³!(!+ "( ( "++-à * { { + «? -+ 1ñ + "( v!! $:ô{ã " " " $#æ&' +!( v"! * ÝR ( " Ì (! = " 9&: $+ K ( " ()+* "" $+ +"³!( v! " + +! " U + â " α - β ã (! ³ =+ -?K { $ ( " " &: " $( +)+ { k } ã Ýb + $ +w "v!*" + $>!!(!#$ &+v!"(*/&: " $( +)+! L P { m }, m = 1,..., M. g! "%v" U % &:"v!+! X&: w ",( #(- +!( v" -" $!! >! 7 -?O= ) Ñ + $+ $ z&: $( +*+!?O $&:!+ "#% ( " ()+* -Î ) {ø ;" [ª ñ + "#x&' =$-àþz $( + ÏªSõ^ [ª Ò ôçý=+-w U!M? &: $( +)+"? & "+!#$, ( " ()+*.*ú4?ov &: $ +-- $(! > %!)r h h... ã ")ù ønög [ª - - z")ø#fù*õ^ [ª,ñó( â; + = U >) $ U õ ö ø ù õ6 [ªW <ùkýp)+"+ / "ª? ã= )( = $(! ( &*w+ -?O +&: - m L P p p... ã "!ö o øm [ª ƒ êö ø ùo" [ª 4Ý = )+-w " / z &:+ -?;&: " $( +)+"? $&:!+ "#ª ( " ()+* K >))++ U z&:(-#$ -?fñó +>&: $- u u v v w... ô{. 8<!#æ&'M+ û " <()!+ * æwk + "( v!! v &: $ û =! > " æwo +&: $-Ñ ) r r s s... 19G [ª2 + = U >) >ẍw% & "+! Þ ( " (*+* ". " "(! w*#$ >) $! k&: $( +*+! 7w"! 7! ù "% $Ïž [ªW o) 7;¹{ö <ù%(! ( {&: $+ -w, { $(!+!7 )!+ / ¹ +!( v! " w* /. ä $! &*Ñ + Ú +", $&: "+", ( " ()+*!$&:+!=$+ + " ( 9&: w* > æw1( = v! $+ $ + "( v!! $ +z( K#$( òý ""!+ U " *! ("> *"+ U K ++ U ". ý =$- + UK " Uv"!(K &: {"+!#$, ( {()+* ( {&: )r# % $#$, + )( +"+ {, ( ( Ñ!v"(*)=! >)+ -w-?¹ ( ÌÝ ( {()+*! $+ +!f f + "!!. u<" "" 'O + " " Ú+, 9 Ñ &" 7&:! >!v" û&: $( ++" Ø /$&: +)!"!%=! $+ + "!à %S ø ö : {ø "% [ [ª2!(-Ñ v! " $ r )à4àz æw "!O +!! / Ì + â - w ' ( * )+ + / Ì &:+" ( + Z= Ñ +-w U ³"(v"! w /!)= *, ;()= + / M {!( "+ b#(+ } $&:!+!#$% ( " (*+* " >-.

27 _ ápüû *,+FG<Z-!+>ž<Z:/02-9DG] PG>ZecA+ :N5 R+_\PS5 R33 > $+"+ " %ñómïê?-! nò7 Þ {* ôk $&:!+! ( " ()+* " "ñó )+! ôî )!+ U!( v"! * Ý!(!#$!+ =$"++ / $++ U Ì! + /!( v! " Á - ) $ w ( + / Å!( v! " $ $à4àz + v!)"yz $ Å ( $ ( /)+ ] $++ U z! nñ + U K"( v! " w ã Ñç $-(!+ + " ( "(+! ñ +! ô{î π )!+ U!( v! " ;Ý π =w ã Ñç"(v"! %!( #)+ "% * $ á / " ("wâ $+ + / w-ñ Ñç!( v! " K(! $ Å)( >)à >ẍw-k"! "+ / "ã π σ Ñç $-(!+ + " Å ( " ()+*!«ÏÐ$&: + $-(!+M+k$&: + ÒÞñ + $ )+ " ô:ýò &: ( "(+-Ñ!;- " nw +!#$,! /yz 7 +"#$ Ñç $(!+ +!#$% ( " "(+* " >-ã π )!+ U z!( v! " KÝï!(!#$!+ =$"+ + / 2pπ ( &' -* #$ " $( )"" ñó )-ôã Ñê!( v! " %$&:+!+%)"" #Ñ Z $&: "+" ( "(+* )à >ẍw )!%& $( +)+ z$&:+! ( + Z= Ñ +-w U f)!+ / Ì!( v" -" w* Ý ( " ()+* "" $+ + U ; Ì$&: +)!" 7 '( = -Ñ )à >ẍwo yz% + "! / 7 + â% {. ƒˆ šo <s ŒoŽu ts Ô lçèžu _,çê? *u_œòäˆv _ˆ O n å) v! $ z ( "! +* "(- (*"!#$Z {(! $+ -wÿ *") * $ 9 {&:")+ -w "v!àª -?!!* Þ $< $" "+ «?7! $(!(!Þ + "#" (!+ + k?m * $ OÝò" $"( wm!!= n-àª $+ ã /! Ñ + "! + X $&:"&: 4 $!( -wª!!=$ -Àª +, X yz" $ +4Á7å< v! "-.g)àª! $&:+)* =$-à Ñ æw o õ ö ø ù õ6 o«ø 7fùo «±" $ º ù[«- K!v"!v!Àª $+ +!O $!( $K!!= Àª $+ $(* Á,u4 $!Î+ "= -Àz $+ + UO# -* ""+ ( 9&r ") w ; "v!!o - %$&:+! + «?Z! Ñ (!(! H 0 = i ßn&:!v"+ $ { Ñ " $(*)!( * =$ /z& w; " (! $+ -w, + "( v!! $ñ + $! k!v"!v!àª $+ f! $(!(U ª"-ô fϕ r = ε r ϕ r, - f = r û! Ç {*- ) ¹ { $ ( " " á&: " $( +)+ ñó #æ&'êv&: $ ( {&: )Ñ k = ϕ r ϕ s... ϕ t r)# Å "1 { $" $( ++" ð+ &* â,àz "v!()=$" +!( (! >)+ Å+! U -Ñ U >wøw "+ + â " (1/N!) 1/2ô,Ý "v"! $+ + Ub! $!(!v { " + + / = + $+ $ H. 0 e k = ε r + ε s ε t ÖK ^Ø où Ú z"â% 7. u > "/&: ( +)+< "+ $yz+ $#$4 ( " ()+* j ( " (*+* " > )*- ) >ẍw -=]&: ( ++-"Þ &: {"+!#$ m = ) $+! +!( v! " $ ϕ r, ϕ s,... + ϕ r, ϕ s,... Î f(i) s j =... Êr rs... m ϕ r ε r ϕ r, "È

28 ñ =&:!"$&: Á"v! / +" z!v!!= + $+ 7&* w! $() = ) $+ î +!( v" -" $:ô *!#æ&',( =Ñ + " + $!= -Àz $+ + «?O $+ $(#$ ZÝP $+ $( #$ + $+)" ªÝ = ) yz > æwo! $+ ( {*Î e m e j = ε r + ε s +... ε r ε s... u< & $( + $ / + "#$! +!Ë $!( Ê!= -Àz $+ Ë Ë $!( Ë"= -Àz $+ X yz" $ +Á-å< v"! "! () "-7!(!#$!(w-&:-< à4v!" Å)( + " $ $+-" "! H =!-r &:",&: {"+ «?Z&: $( +)+!,!+ $yª+ #$% ( " "(+* " >-. ápâá ±Žu,äp,Ž2ä½ O <e*v Œ? =ŒoŽu s _,Žu O?Ô 'é ŠO s O?Žu? šo u o s Žu Ôˆ 'é Œ OŒoŽu œ yšn1-9hgdo\5 5EF L-5EHGFo-} 5ED \;8 \N-9<?>O-;i!u<)+ U;+ $( { w " " * ;#) -!+ )+; "-à 7$&:+ )Ñ Z&:>? + / 7" $(*)!( 7 * K { $ $+% $#$, ] ( b ;v)= * &: ( +)+! H m m m H m "! > { " () " -r) ¹ÉÅ $ $(, â; Zv" k%+ $+ $! / yz %"? { - w-?ú!#æ&' m m à æwk+ v!) $ $ Ê&:- nw + "(v"! w Î m = m, m = Êr r m v" m s = Êr rs m. 6TÔ ø ù "; o 1 {ö <ù6 [ "ø *ù:ö :öô ø#w 4ø;ö; >.>u<())&'- >M $(!! Ê!(w&: Þ" $"(!=Ñ -Àz $+ H + & $ ª $ &:!? + «?Ì {:#) $ «?Ú.Úý $ ( (0 1) = P H P ] ( + /¹ * $ $+! () " ¹!(!#$K!(w&: "( Ì"= -Àz $+ Ë «ym + Á å< v! " - * $(1ÁZu4 $! LP m H (2) H m m = jh jm e m e j Í { m m ( = )à æwë+ %v! $ % $ õkømª ³ + "( v!! w ""Ë {-!#%! = ẍw+ $+ $! / {r# $ U ".*u > ; (!!+, U( "Î j m r = s t Êq qrst m, ""#æ&'«+ $+ $! / Å!-r &: fv! &!" >!! > «&: " $( +)+")!+ $yª+ #$Þ ( "(+* { >- $!!Ñ )à4àz Å æw;&:- nwz + "( v! " w Ê s t st j Î m % m + ( $( j = Êq r qr m, m = m j m ½

29 ò! &á ] ( $< $" "+!#$ #) -!+ +Ê â $ P= )-à4 k û!v"àz $ {* 7 ;+ $ û&:) â%+ b ( *!", U(? " + / M {r)#) $ U ". u<( &'- $ *!+! î {*- * & "+! % ( " ()+* " " *+ " Ý " &: " $(-Ñ +)+ î &:! nw! -w* m!â% æw $&:!+ " / r,+ z!z!+ $yz+ $ m ( " (*+* "" "Î &* w "( " $+ w *!!#$&: ( ++-" P " U+>â &: $+ j = ) )+ $+ -wë)""?ë +!( v"! $ = ) + «?Ë $+w {r m m &: :?Ê $&: *"+!#$Ì ( " ()+* ô()=* + *. u<!! Ë /(? +!³ "! ñ " ( Ñ ) w*à4àz $Ê + 7v! &:. H (2) å (! *, {*- ),ø SE1! K â;& m m m r = s Êq qrs m, &'â O&* wá +!#$1 &: {"+!#$Ë ( " (*+* " >f+*&: æw &: ( +)+Ê "+ yª+ $#Ë ( " ()+-Ñ " >- )à4àz * æwk (! +!( v"! $ K! m K m +) ( $( j = Êpq qr m, m s = j Êr ñ ϕ p ÑX +!( v"! ** + 7=+-w"w+ ; &+ " Ê&: ( ++- $&:!+!#$% ( "(+* { >"ô. ps m j m 2 v") $ 4! Þ! -?!(w&:? w w> æw+ $+ $! / 4 ] ( + U 4 $ $+- --)= U >)à4àz 4+ + Å " + k? {r)# k? ñ {!+ $ +? > Þ $(!+! +U $+!Ñ n H n > 4 + «?%!( v! " w?*ôã &:+) > ( + ]wo( # $+") àò "(!!=$ -Àª + { {&" ª+ &: wẍwÿ ",!+ K $+ $ -Àz! $ $ $( Ì(! $!"(! () "Ê $("!#$¹!(w-&:- û < $" "+! Ê! $(!(û "!* " >-! * U >) $!#$% ; +! # -"v! $(!!" ( "(+* {" -!$&:+! + «?K! $( "(" A = i a(i) m A m A m m 0 "!; % {* w-? m = m m = Êr r m ñ ")" + ( $( *" *"+!#$! $+!ô{.:ý $ >â &'w! +,!Oâ " % {*- ) 7< $!+!#$,#) -!+ )+ = )-à4 ) $ /, Å)( + /K $ $+ L ( P m Am Ã(1) m = jh jm e m e j j + H ) ja m jm e m e j â û )" æwáû+ w X 9 m > æwá! m + "( v! " w ñm {*- ) Þ + k?, $&:!+ k?, ( " ()+* "7Ý+ Þv!* $ Þ $ Ì&: + v!) $ $ ü( $ nwá= )+-w " /! nwrô{ ""M $! {&: vwkk>" v! +) -w$&:+ )Ñ9 &:>?Ñ] "= â+ (? + k?k {r)# k?ú. Ã (1) %

30 Ý ñ Œ \;3 FS5EFG<Z:N5 R]O<?P:8;:;gD-9HSR + :PKPG>4eMgXX-9HRFG3 PG>4e#:Ao-!+_\R%:7+ :3x:NR4H[: :7+0sFKPo\RdQ02-!+ F1A+ :N`D-k <d\n36r :7+o8 \;J anf6eg5q 57:N5 R : QGPGFGb i ÍÅ 9 O?>!wv! }$&:+!v {! $+ + " =$+ +!+ æw Àª æw H $&:!+! M ( " ()+*! " &') 7 ]+ $!!= Àª $+ + / -( "!+ $ "4!+ $yª+ ( "()+* 0! " (w&ê $!( Ë"= -Àz $+ Ë+! ( {&: + ã { Ë $ + %"" +! Z!" &: $+ " nk ( " v) -â $+ " ("w-&á()=!&: æẃ =Ñ = w* ) $+ -w³ì= + +)" w?! ()"! ] «? ( = + " $ $+ ( #$ ³ ¹+( ")à4àz -? $ $+-w-?ú. u<( ³ * $ { {&"+ $"( "+ +" (-!-( Ç ) $ ( O< - (! >)+ $( +!O!+*7 #-() O + â; æwk ()yz+ / ÊÝP $<"( (- $ )Ñ &: *"+! U ( "(+* {!<!Ú ""v!!+ <!-à4 &: " $( +)+ ³Ẍ+ + =$yª + $"= -Àz $+-Ñ + $+ $(#$ -w* - %&: {; 4!+! /. ä &:+) $ { O òv &: $ )( " (!)"!= ) +! <( )Ñ â $+ zw&: $( r+) ò ( &: >ẍw¹ )= " " æw¹+ $!!= Àª $+ + U ò# ""+ )+! / r=! * æw Àª ß )() (! ñó +* * æ?>$&:+! M ( v) -â $+ M"â > æw " "( <?- Xô * + " -Ñ " "+! ª ) â; $+ ª+ $ "= -Àz $+ + «? ( "!+ $ â; O =$ $+ " æw ") : Z#æ&: Ñç+ v! â & * = + 4Ýî!= + + ")ø#f {ö;ì½º ùo$ ) {ø [ *ù^ {e m } : m L P {e j } : j / L ñ U >)à >ẍwo+ $!!=$ -Àª + + / < { w*+ P "+ $yz+ $#$ª ( {()+* ª 4 $+ $(#$ -w* ->!""( U! = /)à > æwk+ -â; 7! $(?+ $K#$()+ } $"( P H 0 P åz $( " UÌ!= #æ w-&1 (!v) $ $yª "* ")ù[ G^"O O!v { -* v) = KK+ $:ô. " + + k? = + $+ H ñ + ( $( ôx! ³"v!()=$" /!v! b $+ $( # - wàz, +! >!!= + -rî 0 {e m } + 7#$"!!(wŸ ( $" ( {&: e m e m = e m + s m Î H 0 H 0 H 0 L P = H 0 + S, S = m s m m E m $"( H 0 $"( $ $(, â%+,+ 7!! " æw!!=$+ +! " $+ -w ] +) $+)" $,+"!"K( = )! " $+" ˆ G : G ˆ L P (A ) = É] {&* $ &+! + "Þ =$ $+ $+ m L P j j A jm m e m + s m e j H 0 H 0 ( "$&: 4&:" )+ " "+! 7!!=$ -Àª + à S ô V V = V S, " $ ³v!)"yz $ $ ³v!!yª < ( y,ẍ&:! # -(! "+.éúv) "+ "; ;+ < ( w* ) w* æwk + =$yª $ ³+ ( "!+ "!(w&: "Î Ω (1) = ˆ G (V ) = ˆ G (QV P ) = ˆ G (QV P ),!

31 " )!. ä &:+* { {&-à4àz $ î "(w&: Z! + ẍ&:! #$!Ì! k* = àþy" QV P = QV P õù:! ù*ø 66Ë(w&'; {r)#) $ «?ÚÎ Ω (2) = G ˆ (V G ˆ (V )) G ˆ ( G ˆ (V )V ) = G ˆ (QV G ˆ (QV P )) G ˆ ( G ˆ (QV P )V P ) = G ˆ ( V G ˆ (V ) ) G ˆ ( G ˆ (V )P (V S)P ) = G ˆ (V G ˆ (V )) G ˆ ( G ˆ L P L P (V )P V P ) + m j j j V m s m m (e m + s m e j ) 2 2ß {* {&-à4àz -? "("w-&:? ẍ&:! #$ v &O w w" æw Z * { ")à4àz -? " Ñ s $+w?ú K"( &:+,+ &: w" æw+ æ?>$&: " { K ẍ&: m! #$ Kv! k K!. 2X= + ) "! ( "!Î!!( #)à4àz æwo "w + -wýü (!v* $ ]M" -Àª - Z ( )Ñ v) $ ]ª" $"( 7< $!+ «?O" ()""(!%-O!>"!"oî ý $ ( û= &r Z * $ &:! $( $ $+ + $(!+ "#, O!+ +!#$; $(!+ + «?K " "w-ñ + Z $ ñó â; / % Žc ôå (,&:" "! + ªv!)"yz -? â 'w-&: $( + «?(! $ { w*+ -w-?ú.u<(! $ "" * $ )&" $( $ $ $+ -wá ¹!+!!"Á -+ Ê&:! + ( 1>"+*< #-(* -ẃ Ö$&:+ " (*)+ = )+-w / f!( v! " w* r"- =!+ + U 1+O( = + «?f7(*#$ $+-"? ñ ã K ( $( Ý φ A φ 2s Ž ô >7 ( (!+ " "+ M ] k?,( $ "w + -w-?,+ v") $ + = Ë + $( #$ -w Ê!!"" Ñ 2p "!" Ì!+ +w ("-( z + %= ) +""Ê!v")! "òñ &:- ( + = )+-w!ê"( v! "!à φ ô 2Ì " " ]v)= * /v &: $ * )!=!)"4+ &: " $( +)+ 7 )/!+*< #-() z Å (! -!+ / ñþ&')+ +! ¹ {*- ) k+ $! / Xô +! /.! & "+! k ( " ()+*!<(*! w*#$ ) > æw7ï + $("+"-Ò ÏÐ!+ +!-Ò7>"+*< #( -w #æ& yz $ ³,! &: ϕ A = φ A α ϕ A = φ A β N = 1/ 2 ( (core)ϕ A ϕ (core)ϕ A ϕ ) I = (core)ϕ ϕ K. &.réx"v"! $+ + U M "!( ψ 1 = N + I 7< $ "+!#$%#) -!+ )+;= ) -Ñ ψ 2 = N I ä #$()+!yz * <!( /!(w&:" )+!+!ª "( ª "= -Àz $+, «ym $+½ÁMå< v!! -! &: / " &: )#$"+!+ / ] ( + / Þ $ $+" H $à Mv") $ + = /= + $+ -wÿ $ H. ÖK ^Ø où Ú É«!v"! $+ + *! $ [î ~

32 Ý H RR H II H NN ~ H NN H ~ II A E (i) (ii) (iii) r 2ß! ( "+ "! $( $ + -w H NN (r) = e N (r) =! > " æw $!( $ H II (r) = e I (r)!!=$ -Àª + á"( ( $+ 1Ý $+ $( #$ " wøàª {Ê â & "v"! $+ + U á= + $+ -w H $&:!+! á!+ $yª+ á ( " (*+* " >? $ > æw.:u<" (! O&: )#$"+* =!Z 7< $!+ U 0 #) -!+ )+! $+ +, ()" -*"+,( $y $ = &' 'Î,!v:! " Ëñ Ž ôåý 1 ψ 1 v) = -; I ψ 2 Ý N,!v:! " Ëñ ŽbŽ ô]ý 1 ψ 1 v* = N ψ 2 Ý I,!#$()+ +!"v)r! { (! * æ? & %v" / (! 7 = $+ $+. ä &:+)<+ + )">7v< *"yz -?ª(! $ " w*+ -w-? â 7 "< * $ &:" $( $ $+ /!+ + "# " $( ] K+ $-("+!#$%( &:v" $(#$" " $( ] R = (core)ϕ Aϕ (core)ϕ Aϕ ñz+)yª $ á ( $( ϕ Ñç"( v! " Ž ô.ú ]Z! U=$"! O( æ? &: $!(!= >Ñ A 2p Àz $+ K ( K ( v) -â $+ O! 7 $( $ $+ -w z H II (r) H RR (r) z + Z! "+>( $+ + -?1"(&:+ " w?1" $"( Ê"= -Àz $+ Î. "v)r! { òñ ŽbŽcŽ ô ψ 1! $!( $&:!+!#$4 ( {()+* v) = N )/ " ψ 2 " > +! +) <<-+ àþ" on o7 U ( " ()+-Ñ R ã ( " -w +O &: {"+! ( " ()+*! ")+ "! æwë ]! n- {* {&:"!+ * ψ 2 $&: ( " ()+* ""; *! «?O! $""(! L P = span( ψ 1, ψ 2 ) "(+* {!,Ýð+)(-yz $+ * æ? &:+" > {!" M " (! $+ -w ( =$- +! $!( 77 $" ] *;?> â; +ª &: *"+! 7 ( )Ñ "+ k?! Ñ (!(!*. 2X k?$& Î!v)r! " òñ ŽbŽbŽ ô7 Àz $ ψ 1 ψ 3 + / û {*" Ú ( {&: )r# $ / " L P = span( ψ 1, ψ 3 ).å<!#æ&' H ( $ ] ( $ UZ-<+ -w ( = ( U " +Z#æ& Ñ M â;ñ r w 1ñ ŽbŽ ôx 1ñ ŽbŽcŽ ô a â 4v! U Ê =&' $ v" X > $ " " $+ + / ]( &:+ " z M+ ( " +>â%+ 4( yz ( $&:!+! ( " ()+* " " "-à M+ $#$ ÏÐ!""( #à4àz $ ẍwz " w*+ ÒMñó+)yª $ Ë {* R ß! 1( "+ k?³=&'?!v" U + 1v" / ( 1!v!+(â æw ] 1f)"Ñê+ v! &:Ë!v)r! " ôfî "

33 a = + $+ Z#$ $! "( -? )() (!z+ $ "= -Àz $+ +wz $+ $( #$ -wz+"!" * $ $+ +!#$ª $&:!+ Ñ #$ "w + -w v) = >ẍw 7+ $!!= n-àª $++ " $+ $( #$ $! $!(;"+ yª+ $# ( " ()+* - Ñ ( * æ?>$&:+! û" Uv"!( +! 4+ v!!" -Ÿ.* â+ -!+ $ + &:"v) " &: {"+! L ( " (*+* "!% Z! $!(Ýü Z ( $&: â, ªM! Ëâ /&>? "!M $&:!+! ( " ()+* P! +!! &: Z ; $ ³ ( " ()+*!! Á " w*+.h.. ÖK ^Ø où Ú g ""v! "v!! Ø (!v) $ Á"(#à Àª -?> æwò " w*+ Ø ( Ø " (" $+ á "(!!= Àª $+ : * =$-à Z ( v -â $+ z+ $!"# "(w&:ª& w 7< $!+!#$#) -)Ñ!+ )+ H 0 = P D H P D + j H jj j k / L D #æ&: $&: ( " (*+* "" ª ( "!( " ( w*#$ ) > æwì+ $"( / ò+v!!( " Á&: $(Ñ L D P +)+! D j Ýò&: $( +)+ 7 + X ( + &* â,)àª.)$&: "+" X ( " ()+*! L D L w w > æwª $&: ( " ()+* " "! ª ( {&r!) w 7 "v!!z + $ +-à "v!*" M+ $v!!yz"#$ P L ) " >,!v " " $+ + k?! $""(! D +) v! $ M+ -=!v"! $+-Ñ P D H P D = P D H 0 P + U = +* $+ -w*. 2 )!!(w&: $!( "= -Àz $+ &* wm D!+!! k?7 < $" "+ «?! $(!( "Z! $(! / M *- * æw ( v -â $+ 7&* w!*+ "!" -+ + $"(""#$!+Ñ +! "!!+ U ñó+ 7 ( +&** â%)àª ôk!v"! $+ + / ³" $""() î L P P D H P D z(-#$!ò = " $ + Uß! k? &} -=f!={&'!yª #$ẍwb ) â; $+ -wb "! ³ -= $+ $+ b $! 7!( (! " = &' zþ " (! $+ ª * " $ Ë 77 $-!+ k?! $( "(". â+ Þ ( {&*Ñ â% $( + {K $&:!+!#$K ( "(+* { "ª?;ö {ød * { M -à4àz -?³+! { w*+ Á *.]84à4 $! / {! " $?-Ì!àÞ> æw &:"!)"" + +" $( Ñ v")!yª O+!( ( " Êà4v"!#$Ì *! "#f " w*+ -w + $&:!+! K ( " ()+* "" ã w + X Ê ( á= &')+ + " M ûẍ&: {r)"ê P (!Àª " X $ Pv!*"yz ()=$ $( + ". L u<( Z!!v " " $++ k?%= + $+ Z 77 $" "+"#$z# ""+ )+M!#ª+ P diml P M "! &')" %!v "" $+ + U f= + $+ -w* 1 )+ "#$# -* ""+ )+- nk!!"" -à4àz "v"! $+ + U U! $!( ÊÝ + k+ " ª! + "ª +*7!( ])?Ñ v"< "w + -w-? * " Ñ.:ÉU)!v!" *,! Á {*- ) w ) w*à æw + "#$! * { + + / M+ "! U z { $ $+!"v!$&:," ( 9&: $+ 77 $" "+ k?o" $(*)!(!* *>!""( U ",! "+ { *!#%v! U; * )Ñ = ")+ Ø&* w( $yz $+ -w ("v) $ b!""( #à4àz -?ẍw " w*+. PSR - +WX- + -9PGëGF6QžH[:+G+ -9D6QGëGF:PGPG>4ežgXwX -9HSR%:3[i/2ð! ¹!³+ $!( ( (!+ +!#$ &*Ñ +!!+*< #-() "++ "#$³ñ - â $ / Ÿ?-(-( -Ñê<"! "!#$ô ( v) -â; + -wÿ - ¹= ) $&: $*! -w &:>?Ë!+*< #-() û $&: "+"#$Ì ( "(+* {K&') Ì"= â+ "! $+ + (! -!+! * z = $+ $+ Þ?-)(" $(M (!+ +!#$ ( ( 9&: $+ ª+)yz * " $ 4 ª!v)r! " Ìñ Ž ô Á ñ ŽcŽ ô.n X"* $&:+) + %= + ")"1! $+ + (! -!+ /Ë!! )*- æwê ( " yª $+ Z= #-( "+ +!#$;= ) $&: $*! -w &: *"+! ( "(+* {! 2 2 ñ K Z&: #$!+ = ) P H P "w + Ë â &f"" - Ë $( $+ -w ô._n Ú+ $!( "f!vr ¹= + $+ 1 â Úw&: $( + «?f( {Ñ H NN (r) H II (r) H NN (r) H ñó!vr " Ü + II (r) ( * {-+ ôþz+ = yz $ ò "v"! $+ +! ò! $!( v&: &:! + (! > O+ $("+* wì!+*< -Ñ P H P #( -w!#æ&' )³+ = yz $ "v"! $+ +! " w*+ ñ ômw w >ẍẃ ( -Àª $! $+ + H H!+ + U 2X-à $+ M 7< $ "+!#$,!= ) $&: $* "" -wêñ ", ;- % {" " + k?k!( ( w -Ñ!+ + «?% < $"" "! > "!-à Àª -?%= ) & $*! àb!+*< #-() Z $&:!+!#$ª!+ $yz+ Ñ #$K ( " "(+* " >"ô )("&: +"+ = $+-w " ") "v" " " $+ +!#$! $!( ( f $(? &,! H $("!#$,Kv") $ 7" / "!(w-& $!( K"= -Àz $+.!

34 é )! * {1!-r&:!1! {&-Àz -? "+*< #( f!+"-à -+ à!1"!v" $+ + " " $ = ) & $*! -w% -?,Ü! *"+ U %!+*< #-() -w ñó - ])( + /, " Ü!( «?; â â v! U"O! ] 'ôuýrùg *ø m ms [à*ù6' ^fn!^[à*ùo G [ªu Ô ø#;"zý! $+ O "! $+ + O! -Ñ U >) æw+4w= /> Þ 77 $"!+ k?;# ""+ )+!M, = $+ $+ Þ -?%!v"! $+ + «?%! $!(! ( K!-à4 $+ :è)! /à4 $+ $< $" "+!#$,= ) & $*! -wÿ. Po\HSRFG3 PG>=-O0S3V[H+s\RPK>=-x36:v`VK.102-9PKF6QWi >â ;!" $ Ú K " )Ñ (w&: + "#" +" $!( ;!= -Àz $+ ;zà4v"! z ] ( +! ª * $ $+"z 77 $" "+"#$ #) -!+ )+/ ( {&r!) w <!v!"m ( " 4 7"r&:!! &:!+ k? &: " $( +)+!4!+ $yñ + $#, ( " ()+*. u > " Ý! $( -wf= " $( +)+ ª&:!?¹ ""!+ «?1 + "( v! " $f+&:! Ê! (">!+ pp hh!+ = U >) $! ZùG :ö; øªùo" o;n;";n ö øm ;M"% $ ¹NÏÂ *ù $yª+ -Ò<&: " $(-Ñ +)+ " >-Î j 2Xr&K&: ( ++-" * æwz ( &: $* " " Ê j pp hh +7$&: +% =/&: ( ++-"M &: {"+!#$z ( " ()+-Ñ j = Êpp hh m ; ] ( + U $ $+# -!+ )+ ";!""(! ³ "(w&: m H (2) (j) m = H m jh jm e m e j + /(! $+%+àø"*"7"" 1 {*- ) " {* m = m = m ñ + ( &:+ M!"v!( = â; $ / ( m m &: " $( +)+ m ) >ẍwk j )( "K +!( v! " $1ñ ô ùõg =wm *ùo¹^ Ê º Î " ""!â; æwì+ $! / Ø =Ñ = Z { yz" * {r Ì â & pp hh H jm m ô. n }!v"( =! / Ú&: " $( +)+ "+ $yª+ $# ( " ()+*!+ " + $+ $!! j =!-r &ª"!Þ/$&: + &: )#$"+!+ /M ] ( + U $ $+ Êpp hh m.u<(!!àª ()" m H (2) (j) m ÉÅ $ $(*ª>!+) ) >) $ / H jm = ϕ h ϕ h ϕ p ϕ p ϕ h ϕ h ϕ p ϕ p u<" )"-h o õ ö! {ø ù õ6 o«ì $!( "= -Àz $+ $+ ( #$ $ = +) $+)" Zv &: Z(Ñ! $+ ;" U(â; w(*! $ ] ( >) $!#$!-r &' ε h + ε h ε p ε p m H (2) (j) m = ( ϕ hϕ h ϕ p ϕ p ϕ h ϕ h ϕ p ϕ p ) 2 ε h + ε h ε p ε p "!!v"àz U+ /< #-( (".! + ") «â U {r# $ U / &: )#$!+!+ «?; ] ( + «? $ $+Ñ m!? m H (2) m m H (2) m w*)w> æw = < &: $( +)+!7"+ $yz+ $#$7 ( " ()+* " >... Ê pp hh m Ê pp hh m "! > "" $++ *.!ÉX- ])( + Uª 7< $ "?<&: $( +)+"" )!( â;&: +-Ñ... + «?; +" "+ / Ì&:- ( + U 1"= v>â;&: + $ Ý ( "z &:" #x"! 79K&: *#$!+"+ «?% Å)!Ñ Ê ( + k?o $ $+"",+ª" + pp hh E(Êpp hh ) = ( ϕ hϕ h ϕ p ϕ p ϕ h ϕ h ϕ p ϕ p ) 2 ε h + ε h ε p ε p Í " " $+ + ) 7ẍ&:! #k+ k) -w 7+4 " ") < "v" " " $+ + «?ª! $!( " H (!$&: yz ; $Àª + àá?;!v"! $+ + «? = + $+ ;+ ).É] {&")"!+ * " $ { ;+! k +" $( -à (0 2) E(Êpp hh ƒ j

35 "!O( = + " ¹ $+ $(#$ ¹ $"( "+ + «?¹ " w*+ ³ñó $+ $( # ¹ "= v>â;&: + :ô '"O ( O!-r &: &: " $( +)+! ³" â+ ³ ( " = )v! U.Þ2X U * { w-w} + U f $+ $( # / â+ Ê!( $ $+ +, #+ "( (!)",") 4&: " $( +)+ 7 :ª! û&:!v>) pp hh m! % - hh ) pp hh E(Êpp K( =!)! /. ÖK ^Ø où Ú u<( &: $ ì ³ Ç $ ìâ K! /!$&' U ]+ = (-!ẃ " (*!û!""(!#$f!(w&: "( K!!= Àª $+ «ym $ +Áå< v! "Nî áp> Ý _,Žu O?ÔĨ š6 œc, Žu ˆ O ˆ œc s w O?Ô O o _,Žu O ˆ Ô ŒoŽu,äp,Ž2ä½ O š6œc šoˆ Žuˆ Ĩ œþšk œc p WŽ2 Ô ˆŸž ous sˆte s OšK ä #$()+ Åẍwf$&:+ ß ( ( " / &: $ "+ ( (-à Àª ß( )O"+ $ f $< $ "+ «? " $(Ñ ""(!,,<"( (! "> $&:!+ k?o $&*?>$&:!,K" + àî $"( "+ +!#$% (! $+ -w ) $. ±:f02-edg]ty :f0sfkpògd-ehsr+ :PPo\1:f0sFGP5\bSR}s0sD^Q<Z:D-9HVDG> grfgd-9po\6i>u< "( " Ë $ +")( +-à $&: 4&* w," * )+ -w% )( + = yz -?; { $(!+ + «?% " w*+, $- - $+7 9 {&-à4àz!v"(*)=! /.*u ÝÇ (!(!#$!+ -= ")+ + / Ñç"( v! " O-# $( &:+ «? φ A φ 2pπ! " Ý!v!()=$à M+)v!"()!+ k? "( v!! $ Ñ!( v! ",( $ ] ( àþ> æw%-," "" )Ñ σ + U "ã $&:!+! ( {()+*!1( w #$ æw³)! ÏÐ+ $"(!+ U -ÒZ&: ( ++-") Ý ù[ cô ø :öu; ù[ ¹ xö;«ø A = (core)ϕ A ϕ A = (core)ϕ A ϕ A = (core)ϕ A ϕ A = (core)ϕ A ϕ ñ ϕ A = φ A α ϕ A = φ A β Z. &. ô{.-8 A! ) > æwo!!+ «?%&: " $( +)+-Ñ "" = + $+ $ ( " $ *+ "#$% +-ã= )v! &: $ ³,+ -?O+ª+ $!( " 7 "( nwÿ. u< %!!" "! < (*! -r) É] $- $( A H A = ϕ A ϕ ϕ A ϕ ϕ A ϕ ϕ ϕ A = φ A φ φ φ A = K ñ $( " U &:>? + /f +" $#$(Ë (" &') ( ¹ + $#$( ("+ 1 +!! / ß $( $ $+-Ñ + U /ã!""("oýç!v! $+ + UKÝÇ +" $#$(= )" {&:! % ) â " $+ * } #$%+ = K + + ])"( ï +"#$f# ""+ )+¹+Ì $&:!+! ( "(+* { "Áñ ¹ f ] ( ô{ "#$(Ñ ( v) -â $+ -w $(!"#%!(w&:m& w 7< $!+!#$,#) -!+ +"ôk $ %! & ( e0 K ) #æ& K e 0 Ñ &: )#$!+ *"+ U ])"( + /K $ $+.[Í!v { " + + / 7=$+ + -w e 0.*å< { â+,-v! {&: "ẍwÿ * "%+ = yz + $+ à "! > "!" Z!v "" $+ +* w -+ -w e 0 + K ψ T = 1 ( A + A ) ÝD + "! Ý ψ S = 1 + "! / + # 2!. E T = e 0 K E S = 2 ( A A ) Ý "

36 ý =!+ + ( {&: )â% >â+ yª Ê "r&³ " ()!Ë!(!#$ "("w-&:ê+ {&: Ñ #$!+"+! á ] ( + " Á $ +"Áv! &û "+ " û"!!yª $ æwò!û!+ $yª+ $ ( " "(+* " " ÏÐ!+-Ñç (+ / Ò &: ( ++- AA Î A H (2) A H AA AA H A (AA) A = e 0 e I #æ& ÝÄ+ $ "= -Àz $+ +wì $+ $(#$ -wì!+-ñç )( + "#$,&: $( ++! ñ " + e &:) â+* v! U"Ì"" +Ì!>"Ëâ ô. u<)!=$w Ì " I! $+ + U ³!v!!= + $+ w* n= 7 ( $ / " ñ &:" 7 $( {")+ "! z&: $( +*+!?' = +)?(+ -: æwrô AA H A = AA H A ñó $( " $( + " + 4ô = AA H A A H (2) () A = AA H A K * { =! {&:!,!"( $+ ã ( +K!-â <= +) $+ "-r & ; Ñ! )â% * $+.UÉÇ! + "!à &:Ë!""(!#$Ê!(w&:f" $!( á "= -Àz $+ á "-à4!+ ] ( Z# ""+ )+ â+ ;= ) *,) ( ) e g, g = K A H (2) A g e "v!+)(>â%! "<!"+ -!+ " U ) â; $+ / + #!4 "( -!4( $# ( æw; " + "! ()" ã> ª ) $ " - $+M"+*M+z ) " f&: 4=$+ -!+z Z ( $! /y ) A H (2) A K -")K ñmô øªùo"; Gª?«z;¹Ew [ [ª?«ù[ *ø# Üö ô«+ "yz 7+ w. g \8 PGFSRPK>pb 87\;<?FGDG]R :PGFo\P [\b[v-9p` -!+87\Kiu $ ( P â; $ î ( {&: ") " "Ì Å)( 1 Ñ < $ "+!#$,#) -!+ )+;;v)= * 4&: ( ++-! H = e g ñó "v"! $+ + U 4= + $+ -w -("!+ $ $+ $( #$ e bc = e g/2 ô{ = * g e e + g, e g, e g, e g H = e bc g e g 1/ /2 A, A, A, A e g ô > -! «&: { ª â $+ $+-( w-â ñ } $&:()=- $ $ / " w*( +* w " { + &:! + â,) > æw+; {&: + +-à ] ( )Ñ e! > "!-à Àª $K( = $( + " " :ô. bc 2} $&:!+ " ò ( " ()+*! " Ï $&: +Ì (!+¹+$&: +¹ -!Òª! ( {&: Ø(?>" )Ñ + $+-+ /O" ()""(1 *ùg :ö1ô ø S :ö# :ö% æö«*ø ô«{ {&à4àª "v!()=$" /Î ( &: $*! A (s A ξ K! "+ $+- b!#$,! $(!(Kñ ξ = x, y, z -* 0, +, ô«+ v)= + /Z&: $( ++ +!( v"!* -!"+ ẍw*à w* æwoo )" A >= ) $+-w* $ æwo+z( =$" z&: $* " " -w ξ O>" )Ñ + $+ ß"v! / + "#$,$&:+! $(!+ +!#$%! $()""(; + +!O +!( v" -"*! 1/2 1/2

37 (! $ " ") >ẍwv! =M -= $+ $+ -w. â%+ Þ-v" 9&: " æwÿ " * { $+ +* wª ] ( / " { {&:+ $!!"+ "yz $+ Ý} " ( " Þ&")Ñ $+ +* w; ])"( < w*( +"#$7 (! =! {&: $+ -w% + $-(!+ +< ) A ; { $(!+ + " (s A s ) ; { H = e bc g(s A s ) ÖK ^Ø où Ú u<" "( "" X ])"( (s A s ) v> = * &: $( +)+! A, A, A, A ] &: ; &:!v"+ ; )= " ẍw! $ " >&:+ /!+!yª $+ w* Z&*w 7 $( $+. +-Î s A+ A = 0 s A+ A = A s Az A = 1 A O!. &. s 2 Az A = 1 A 2 ] ( v* -â; $+ +"#$ $< $" "+!#$ª#) -!+ )+7&')!+ (!ª * =$>Ñ æwz ( z" * + ª ])#$+ + «?ª "!* "" ("&: k?7 Kñm7ö E *ù*øn [ª?«T {ö ù6 [ ø# *ùö; K rö«$ o¹;m8w {öô{.é«!!*! $+ +! Ñç $&r * $ - $+*7(!+! /= + $+ Þ 77 $-!+ "#$ π!v" + + "#ª +" $#$(r?-)() $( + 7&* *< $( (! ]#$+!Oñ $+ $( #$ " Z! /#$$&:+ )+-Ñ g " (!+! â $+ M + ", * $(!+ ",+ {&:+ -? )"?ô{. ï7 + "M" + 7< $!+ UZ#) -!+ $ ;!" ( yª $+ +z")-à â X<!( %ñó "v"! $+ + U X! $!( Ë + "!à " ( {&: w*àþ> æwz ( $M= &' :ô U= +* + -w )() (< â+ 7" ( {&: =«Ïê! + k?>òñ &:! > " / " $ $( $+!!+ «?ôn= + $+, $+ $(-Ñ #$ K+ -= yª -?K + #æ +!#$, O( - "+!#$% "w + Î g = (E S E T )/2 e bc = (E S + 3E T )/4 u() "( = )! * æw ;;!"+!+ "#;(! â $+ -w! + «?w&: $(ZÝ. e bc g + $Z $( â r!+ ª z= )! * " (! $ " w*+ â ] 4.N $ " &*?$& ()-Ñ â+( ( " ()+ +K (- $+ +--àç>"+*< #-() à ) $ ñ {! >%Ï 2pπ v &ª= + "( v! "!Z!! $(?+ "!àª >M!""(", â% ;! W Z " {&:+ "( v! " -Ò 2p! á!$&:"( $&'"ô.-ý )r# $ $+ -w Z!" $+ "+ k?!! $(?+ " $ + =$yª -?K + # +!#$, O( - +!#$% { w*+ â%+,+) -+ e bc (r, θ) = (E S (r, θ) + 3E T (r, θ))/4, g(r, θ) = (E S (r, θ) E T (r, θ))/2 ±:/02-9DGF+ :3\;PGF-;i Ü +"#$ + / P!v!()=! â%+ Ê! ( {&: { Ê $&:!+ " ( " ()+*! ÏÐ$&: +Ì $(!+¹+Z$&: +f $ÒM&* w¹ ) $ 9â%+!#$! (w-â; $++ $!$&:"( Ì )Ñ "( " " "! > "!à4àª 7< $!+ /# -* ""+ )+.:ú<+ ( + $ " $&:+)* * " ("v!" ) (!- (!), < $" "+ UK# - ""+ *+! * /)à4àª K +!!+ " K+ = ) â,àz!!=$v!>â &: $+ + U " w + -wf!>"¹ $- -!f#-= $+ v" ( #$" " -? &:>? + k?¹ ])#Ñ + "+ k?o# -""+ )+! &* wk )( )!ñ -# $( $&:+ «?!!ô H = A> H A = (e bc (r A, θ A ) g(r A, θ A )(s A s )) A> u<$&*?>$& " +! >)+ + UZ+7 * )= ")+ (!- ])+ 7 >!)= : æw " + Þ $yz+ / /. Í #$M( )+ + "++ /+7! ( {&: -+ e bc (r, θ) g(r, θ) = $- $( $+"!+ k? +&: {â+ «? ( + «?&')+ + k?ëø E[ ^#weo N%oxÔø ù6 :öý =;+) v") $ ª! + k? ( 9&r Þ" ( 9&: $+ -wz#$ $! ( z * $ { {&:! >)+ -wz) /"" * { X Åv!)"yz ª) - -Ñ!&') :ôr $ª! (wâ $+ + «?<-# $!$&:"( &:! ã( =$- + Þ!" (! = "$&*w> æwm <?-)() $( * { + =$ {â%)àª -?O!!=$v!>â &: $+ + «? { w*+. w -" -?K "(-"-(K =$-à æw! + = $- "!K!!#$ >" $&:!à Ý e bc (r) = e &* w )( 9&:+ -? )! g(r) = g e bc (r) = 0!,"?O {""+ «?K {*- w? g(r) = 0!#æ&'ª ])"( #) -!+ )+, ") >ẍw ( {&: *"+, ( " Î È

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