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J ?@H¹WJ ¤ KÞª <L> ¦ ¹ ¦ KjXA9LH ¦ GL?“:9 ¤ HA?@H ¦ K ¤ HB©:K ¤ J;¨ ¦ K§GIH ¦ ¹WJ;«#« ¦ > ¦ 9;º;J;:#KjXA9LH ¦G¢ \ :@> ¤ :@KM:@>;: ¤ J Aœ £ : ¤“¦ €EF>;:@?@9 ¦ 9;J ¦ ?7«#H@>;¾ ¦ s*:C¹WKMH@9T: ¾ O©9T: HAK§9;H@? ¦ <;#H K;EF¨ ¦ 9©½9LH ¦ :KMJ;¾< ¤ H ¤ JLG;J¬<L> ¦ ¹ ¦ KjXA9LMH _§H HA< ¦ >T: ¤ HA>;:çK ¤ >;H@J ¤ KÞª ¤ H@¨;9LH ¦ > ¦ Z ¦ 9;J ¦@œ\ E“K ¤ X¢¦ J KYXGL ¦ > ¤ H@?AH#<L>;H@K ¤ >T:9;K ¤ ?@^H O¢¦H <;>LHAJ©­®?@cH KjXA9LH _§AB(H) : KY_ LC½>;: MH _§>T:9;JL¨ ¦ 9L^9 JB H@< ¦ >;: ¤ H@>;H@?=¹ ¦ ¼;K ¤ ?–AE N3Q7J©Bw? H O ΓS (L2(R)) ¢ K§J;¾¾ ¦§¤ ½>LJ;¨;9LH ¦ «#H@GIHA?@KMGIH ¦ <;>LHAK ¤ >;:@9LK ¤ ?AH œ µ :KMKM¾H ¤ >LJ;¾ EF>T:?@9 ¦ 9LJ ¦ j¹ KLªúH@< ¦ >;: ¤ H@>T:aM?A#H KYN´º;J;J UtdUtT › U= iHUt , U (0) = IdtK1_˜:@¾J"KYX ¤ HA9LJT:9;H@¾ H O_¹ ¦ ¼;K ¤ ?–EAN3Q ¦ ¾ ? ¤A¦ 9F­HA>L9;H@¾ <;>LHAJ©­®? ¦ ¹ ¦ 9;JLJ H =¦= H ⊗ ΓS (L2 (R)) Oj_â¹T¡ UH = H0 ⊗ I − I ⊗ i∇ + H©ª¬« ,<L>;J;¨ ¦ ¾H©­ª®« = K ⊗ Λ(g) + R ⊗ A† (g) + R∗ ⊗ A(g),¢¦¦¦¤K ∗ = K O H0∗ = H0 J R HM_§>T:9;JL¨ 9L9^J HA< >;: HA>HJOZZ†Λ(g) =dx g(x) a (x)a(x), A(g) =dx g(x) a(x),A†(g) = A∗ (g) O g ∈ L1 (R) ∩ L2 (R) ∩ C(R) O a(x)Ja† (x)¢ <AKTH ¤ 9;H@K ¤ JH@< ¦ >T: ¤ H@>;H@? EF9;JL¨ ¤ HqS ¦ 9;J©ª¬J¬>;HqS=¹ ¦ 9LJFª œ± ¾ ¦ K ¤ H «J;GIKMJL>;H@?“:9;9LHA¼q«,EF9;G;ºLJ;J O?–B H¹;ª^Q ¦ ¼q? HA<L> ¦ ¹ ¦ K ¦ 9;J ¦ _˜:¥½g¾AJ KjX ¤ HA9LJT:9T: H©­ª®« OgL–E®¹ ¦ ¾ >;:@K§KM¾À: ¤ >;JL?“: ¤ XzK ¦ ¾ ¦ ¼;K ¤ ?@Hz9 ¦ H ¤ >;J;º;: ¤A¦ KjXA9HJB«#JL9;J ¤ H9 JBi«*EF9;GLº;JL¼ gα(x) ∈ C ∞(R) O α ∈ (0, 1] O+GIH ¤ HA>LH ¦ J;¾ ¦M¦Œ¤ <;> ¦ ¹ ¦ ½0KTHA¾~¹ ¦ KjX ¤ :¥½¿«*EF9LG;º;HJ N;Œlimα→0Zf (x)gα (x) dx = f (0)¹^K;ª KYNRLAH@¼ 9 ¦ <;> ¦ >^J?A9LHA¼ HG_M>;:@9LJ;¨ ¦ 9;9LHA¼ «*EF9LG;º;JLJ f Oz<L>;J;¨ ¦ ¾ ¹ŠJ;:C½¾ ¦§¤ > dg (α) 9LHAK§J ¤A¦ KLª¬«*EF9LG;ºLJ;J gα K ¤ > ¦ ¾J ¤ KÞªÁGD9FEKYN<;>LJ α → 0 œYv «#JI½­J;¨ ¦ MK GIH@¼ ¤ H@¨;G;J ­®> ¦ 9;J©ª`O ¤ :@GIH@¼k<;> ¦ ¹ ¦ K¬K§HAH ¤ ? ¦Œ¤ K ¤ ?–E ¦Œ¤ ¾H¹ ¦ KTJ ¤ H@¨ ¦ ¨;9LHM_§Hš?–­¥:J;¾H¹ ¦ ¼;K ¤ ?@J ¦ ¾'K§J;K ¤“¦ ¾gJ†K7H@G;>FE!S ¦ 9LJ ¦ ¾ œ ¸ HA>L¾À:#KjXA9HJ ¼ <;> ¦ ¹ ¦ KiK ¦ ¾ ¦ ¼©½K ¤ ?A: _˜:¾JAKYX ¤ H@9;J;:@9LHA? lim H©­αª®« ª;?#K;ª ¦Œ¤ KÞª1¯°^±^²³G´Hµ!¶D±F·*¸!·#¹º‡³j»„¼±H±^½€º¾·¿DÀÁα→0¶Â!Ã#·d¶`·º€O ¤ :G=G©:Gç> ¦ ­§EKjX ¤ : ¤#¦ _MH¹ ¦ ¼;K ¤ ?@JFªç9T:,? ¦ G ¤ HA>HJ ?@J©¹Š: ψ(v) ⊗ r OG_â¹ ¦¢¦ ¦ ¤¦ ¤¦ψ(v) ∈ ΓS (L2 (R)) GIMH _ > 9 9^J¼D? G H@>`O v(0) = 0 O r ∈ H OF>T:? 9 9FEKjN;O: KWJL9 ¦ ¼L9T:CªwMH L@cH KTHA¨LG©: ¤ :G;J©BD? ¦ G ¤ HA>LHA?ç<"KWH ¤ 9;:=? H œ;± ¹Š#: KjXA9 ¦ H¼ Z ¦ 4¾ OG_â¹ ¦ a ¤ H,9 ¦ <L>;J;?@H¹WJ ¤ G <FE ¤ :9;JLº ¦ OGL–E®¹ ¦ ¾zH@<FE“KMG©: ¤ X,J;9I½¹ ¦ GIK α Mœ v KLEF¨T:`¼ OGIMH _⹊:,H@< ¦ >T: ¤ H@^> J K O R J H0 GIH@¾¾/E ¤ JL>FAE N ¤ O–>;:@K§KM¾H ¤ > ¦ 9? Ä ŽÅ œ ± ¹ŠJLKMK ¦ > ¤ :@ºLJ;H@9;9;H@¼=>Tc: LAH ¤“¦ >;:@K§KM¾À: ¤ >LJ;?A: ¦Œ¤ KÞª GH L@MH LGQ ¦ 9;J ¦ 9T:K KLEF¨T:¼b9 ¦ GIH@¾À¾/E ¤ J;>©AE N3Q7J©BÁH@< ¦ >T: ¤ H@>;H@? œµ :KMK§¾ÀH ¤ >;J;¾ EF>T:?@9 ¦ 9LJ ¦ T › UÁ?…<L> ¦ ¹ŠK ¤ :@#? K ¦ 9;J ¦ ?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AJ©`ª O´<LH–½>LqH S=¹: ¦ ¾H ¦ H@< ¦ >;: ¤ H@>;H@¾ Hb0 = H0 ⊗ I − I ⊗ i∇ O;9 ¦ ­¥:?AJLKÞ^ª Q7J;¾ H ¤ g ŒK_˜:¾ÀJ"KYX ¤ H@9;JT:9;H@¾e (t)dUe (t),= iH(t)UdtbT} Ue (t) = e−iHb0 t UtUbH(t) = e−iH0 t H©­ª®« eiH0 t_⹦TŸ U= K(t) ⊗ Λt (g) + R(t) ⊗ A†t (g) + R∗ (t) ⊗ At (g),K(t) J R(t)>;: ¤ HA>LHA?:*H@< ¦ >;: ¤ H@>^J¢ 9 ¦ <;> ¦ >^J?@9^J ¦ <LH*9;H@>;¾ ¦ K ¦ ¾ ¦ ¼LK ¤ ?“:,HG_M>;:@9LJ;¨ ¦ 9;9HJB=H@< ¦ ½K(t) = e−iH0 t KeiH0 t ,R(t) = e−iH0 t ReiH0 t ,¤¦Λt (g) O At(g) J A†t (g) = A∗t (g) ª;?#K;ª^N KÞªç9 HM_§>T:9;JL¨Z−t∇t∇Λt (g) = e Λ(g)e =dx g(x − t) a† (x)a(x),Z−t∇t∇At (g) = e A(g)e =dx g(x − t) a(x).¦ 9L9^J¾J`Œ± G©:¥¨ ¦ K ¤ ? ¦R¤ H ¤ :KYX@9;HG_MH¾9;H¥S ¦ K ¤ ?“:AO­¥:¥¹:cN3Q ¦ _§HHML#KŠ:K ¤ XH@<;> ¦ ¹ ¦ K ¦ L9 JFªŠ¹ :@9L9^JB¬H@< ¦ >T: ¤ H@>;H@?HOT?AH–­qX@¾»M¾pKWJL9 ¦ ¼L9FEANtHML@H#KWH@¨;GFE Lε ¾À9LHqS ¦ K ¤ ?A:EεS = φ(f ) : φ(f ) ∈ E S ,kf kB(H) 6 ε, kf kB(H)⊗L2 < 1, f ∈ W21(B(H), R) ,¦ S ¢ ¾9;HqS ¦ K ¤ ?@H GIHG_ ¦ > ¦ 9EKTHA¨LG©: ¤ :@GIHG_MHú¾À9LHqS ¦ K ¤ ?A:#<AKWH¤ HAH> J ¢ K§JAKjXA9LH 9 ¦ <;> ¦ >^J?A9LH ¦_⹤ ^9 JBv? ¦ G ¤ H@>;H@?^Oœ¦0 < ε 6 1 r#J;9 ¼;9;:–ªvHGLAHC½¤ 9T:ú? S¤¦ ¦ ¦Γ (L2 (R)) Æ >T:KMKM¾À: >LJ;?A: ¾]J H@< >T:¥½<;H t K ¦ ¾ ¦ ¼LK ¤ ?AHkH@< ¦ >;: ¤ H@>;H@?^OT¹ ¦ ¼LK ¤ ?EANRQJ ¦™J©­EεS?ΓS (L2 (R))œDv <;H@¾HMQ;XMN†9 ¦ M_ Hç?@? ¦ Š¹ »M¾ KK ¦ ¹TEANRQ EANt9LHA>L¾/ED?_â¹ ¦Sp(X) = sup kXh ⊗ ψkH ,ψ,h<L>;JL¨;»M¾ψ ∈ Eε , h ∈ H,HŒTŽ UkψkΓS = khkH = 1.?AH@¼;K ¤ ?A:v<;> ¦ ¹Š9LHA>L¾gJ ¹jKLª p(X) <L>;H@? ¦ >“ª^N ¤ KÞª{9 ¦ <;H@KM> ¦ ¹WK ¤ ? ¦ 9;9;H œv ?@HA¼I½K ¤ ?@H 9;H@>;¾]J p(X) = 0 ⇒ X = 0 KK ¦ ¹TE ¦§¤ J©­'KWJL9 ¦ ¼;9;H@K ¤ J >T:KMKM¾À: ¤ >LJ;?A: ¦ ½¾]JB H@< ¦ >;: ¤ H@>;H@?J ¤ H ¤ :#KjXA9LHAK ¤ J ¾9;HqS ¦ K ¤ ?A: E S œcl H@>;¾À: p(X) HA<L> ¦ ¹ ¦ KLª ¦§¤εKTHAG©: KYX@9;HçG? J <©EFAG KLEAN ¤ HA<LHcKTHM_§J^N? H œRtRt\ E“K ¤ XœKΛ (t) = 0 K(s)Λs (g) ds J Kg (t, u) = 0 K(s)g(u − s) ds\ #H KWqH S JL¾vR(t, u) = e−iKg (t,u) e−iKΛ (t) R(t)eiKΛ (t)JÁ>T:KMK§¾H ¤ >;JL¾K ¦ ¾ ¦ ¼LK ¤ ?AHçH@< ¦ >T: ¤ H@>;H@?( ZtZτZiK(t)Λeα (t) = ef∗ (τ, u)R(s,e u)Uexp − dτ ds du R00× g(u − τ )g(u − s)v¦)Zt Z†e× exp i dw a (w) dτ g(w − τ )R(τ, w)0Zt Z∗f (τ, w) a(w)g(w − τ ) .× exp i dw dτ R0¾ ¦ ¼LK ¤ ?AH´HA< ¦ >;: ¤ HA>LHA? Uα(t) GIH@>;> ¦ G ¤ 9;HH@<;> ¦ ¹ ¦ K ¦ 9;H,9;: Lε(H) = Lε ⊗H O¦ _MHY­®:@?@J;K§J;¾H@K ¤ X{H ¤¦¦ ¦ ¤œl :@¼I¹Š»M¾α HGLE“KKTHA?#K 9T:^K ¾ ¼;K ?@H@¾ «*EF9LG;ºLJ;¼ gα:KMJL¾À< ¤ H ¤ J;GFE~>;:–­> ¦ Z :cN3Q ¦ _§HiHA< ¦ >;: ¤ HA>;:"EF>;:@?@9 ¦ 9;J©ª ~ >L»˜¹WJ;9^_ ¦ >;:iK_˜:¥½¾AJ KjX ¤ HA9LJT:9;H@[¾ TŸ U œ”¥ˆc͉nΖ‰Õ‰˜’”Ï9ÐÒÑ#ÓPÔÖÕL”#×Ǝ;ΌAØ YÙÛÚqÜ?ÝÁ‰dލT’WjÞAߏ[IUWdc[Ib*ÈQ ÇDIÊÉ`I‡Ë-Ì •Œ— ‘H(t)•’jÜ?ݍÏ@‰à“— ”Í”Ïψ ∈ EεS á h ∈ H•ŒˆcÍFŽGÏ@‰dΌWDÏ@Ž •Œ©W‘“’Ž¥Ø ”¥‹‰˜’YàIŽt+∆tZoneα (t + ∆t) − expeα (t) h ⊗ ψ UH(τ)dτUtH√3/2= O ∆tC1 (ψ) + O( t ∆t) C2 (ψ)√ √ √+ O(min( α, t, ∆t))C3 (ψ),×Ζ‰’‰à©”®—ç”ÍDÜ·‰úˆ”ޏ”qろT—ç‰ÕW‘“’YÜ·‰-ä Ì ’Yà“‹WŠ”¥’ŠŽYÜCj (ψ) á j = 1, 2, 3 âµ : KMK§¾·: ¤ >;J;?A:Cª “¤ ¦ < ¦ >^X{H@< ¦ >T: ¤ H@>¦¦b eU (t) = eiH t U(t) O3<LHcKLEF¨T: ¾ KK ¹;½K ¤ ?@J ¦ ¹:9;9LHA¼ ¤“¦ HA> ¦ ¾]J œ”®ˆGÍö‰dÎC‰Õ‰Œ’Š”9ύÐçænÓÔ3ÕL”#×ΖŽÎŒAØ YÙÛÚÜ?ÝY‰dލW’TYÞ"ߏ[IUWdc[Ib*{Q ÇDIÊå`IÖË*Ì •Œ— ‘Hα’ Ü?ݍÏ@‰ à“— ” ͔ Ïj•Œcˆ ÍFGŽ Ï@d‰ ΌWD Ï@Ž •Œ©W‘“’¥Ž Ø ”¥‹‰˜’YàIŽS0ψ ∈ Eε á h ∈ H×Ζ‰k(Uα (t) − exp{iHα t}) h ⊗ ϕkH = C1 (ϕ)O t3/2 ,’‰à©”®—ç”ÍDÜ]è ˆ”ޏ”qろT—ç‰ÕW‘“’YÜ]èC1 âÔSΓ (L2 (R))ä Ì Y’ à“‹WŠ”¥’ŠŽµ :KMK§¾ÀH ¤ >;J;¾ <;> ¦ ¹ ¦ vK K ¦ ¾ ¦ ¼;K ¤ ?A:=HA< ¦ >;: ¤ HA>LHA?UαáΖ‰è•˜—Ï Ì Ù4é Y èÏ<;>LJlim gα = δ(x).±_α→0>;:#S ¦ L9 J ¦ ¹jKLª7¹ ¦ ¼;K ¤ ?@JFª <;> ¦ ¹ ¦ KYX@9;HG_MH*H@< ¦ T> : ¤ H@>T:9T:<;>LHAJ©­®?@HcKjXA9HJ ¼ GIH–½¦ > ¦ 9 ¤ 9^Jw¼ ? ¦ G ¤ H@> ψ(f ) ¾HqS 9LH ­®:@<L;J K: ¤ X ª;?AL9 H^ŒJψ t (f ) êW=ëíì lim Uα (t)ψ(f ) = exp{i(H0 )5 t}α→0 × exp − R∗ (exp{iK} − iK − 1) (iK)−2 R 3 t t Z∗iK−1× exp i dτ R e − 1 (iK) 1 f (τ ) , ψ f t<L> ¦ ¹ ¦ KjXA9;:–ª¬«*EF9;GLº;JFª0f t (x)>T:?A9;:f t (x) = r(x) (f (x + t) + h(x)) ,›šTà U<L>;J;¨L»M¾h(x) = iI(−t,0) (x) 1 − e−iK (iK)−1 R 2 ,r(x) = exp i (K)4 I(−t,0) (x) .¦ IG KnJlEDH@< ¦ >T: ¤ H@>;H@? H@<;> ¦ ¹ ¦ K;ªHN ¤ <LHA>“ªI¹ŠH@G¬J©Bk¹ ¦ ¼;K ¤ ?@JFª œ± J¨;J;KKWJL¾ G;>;: ¦ ?AH ¦ E KKWH@?AJ ¦ O_GIH ¤ H@>;H@¾/EYE®¹ŠH@?cK ¦§¤ ?AH@>“ª ¦§¤ <;> ¦ ¹ ¦ KYX@9^J¼? ¦ G ¤ H@> K§HAK ¤ H®ªL9;JFªOI: ¤ :GAS ¦ <;> ¦ ¹ ¦ KYX@9^J¼9_ ¦ 9 ¦ >T: ¤ H@> K ¦ ¾ ¦ ¼;K ¤ ?A:*_§>FEF<L< Uα œz ¨;J ¤ J?“:Cª ¤A¦ H@> ¦ ¾/E › J ¤ H ¤ «ú:@G ¤ O®¨ ¤ HR_ ¦ 9 ¦ >T: ¤ H@>îT ¡ U+9 ¦ ­¥:?@J;KMJ ¤ H ¤ ?A> ¦ ¾ ¦ ½9LJ`OŠG;>T: ¦ ?@H ¦ E K KWH@?AJ ¦ J <L> ¦ ¹ ¦ KjXA9HJ ¼ï_ ¦ 9 ¦ >T: ¤ HA>v¾HqS 9;H 9T:¼ ¤ J JLKM<;H#KYX–­ME@ªK ¦ ¾ ¦ ¼LK ¤ ?AH Uα(t) œ ³ <;> ¦ ¹ ¦ KWJL¾…K K ¦ ¹;EAN3Q7J ¦ KM< ¦ º;J;:#KjXA9HJ ¦ H@< ¦ >T: ¤ H@>^JlEF9LJ©½¨ ¤ qH S ¦ 9LJF`ª Œo,9©¹o´­9T à U KKv ∈ W21 (R \ {0}).A± ψ(v) êW=ëíì v(±0)ψ(v) ,¦ ¹;E Œ¦ ¤ OT¨ ¤ HA− ψ t (f ) =eiKf (t) + i eiK4A+ ψ t (f ) = f (t)ψ t(f ),4H ¤ G©E®¹:=<;H#K;EF¨;: ¦ ¾GL>T: ¦ ?@H ¦ E KKWH@?AJ ¦ ¹^K;ªu KLª¬?MJ?@H¹:(1 − e−iK )(iK)−1 R2ψ t (f )ψt ŒA− − eiK A+ − i(eiK − 1)(iK)−1 R ψ t = 0.Tš U<;> ¦ ¹ ¦ KYX@9;HG_MH=EF>T:?@9 ¦ 9LJFªDEF¨ ¤ »M¾€OT¨ ¤ H∂∂I(−t, 0) (x) = 0−∂x ∂t<L>;J x 6= 0 OöH ¤ GFE®¹Š:kKK ¦ ¹TE ¦§¤ Oö¨¹^K;ªw:>^_ŒEF¾ ¦ 9 ¤ :=GIHG_ ¦ > ¦ 9 ¤ 9LHM_§H² :@GLJ;¾ HGLA>;:–­HA¾€O;<LHcKLEF¨T: ¦ ¾¤ H ¤ : GIH ¦ S ¦ MK H@H ¤ 9;HGZ ¦ 9;J ¦ ?MJ<;H#KW9©ª §¦ ¤ ÞK ªiJ? ¦ G ¤ H@>T:AŒ∂∂f t (x) = 0.−∂x ∂td t ψ = ∇ + i R∗ (eiK − 1)(iK)−1 1 f (t) − i(H0 )5dt− R∗ (exp{iK} − iK − 1) (iK)−2 R 3 ψ t .›A›K ¤ > ¦ ¾ƒK;ªFªztGÁ9FEKjNtJDEF¨;J ¤ J ?A:–ª¬GL>T: ¦ ?@H ¦ E“KKWH@?@J ¦ TO JL¾ M¦ ¦ ¾dU (t)ψ(f ) = −i∇ + R∗ (eiK − 1)(iK)−1 A+ + H0−idtt=0+ iR∗ (exp{iK} − iK − 1) (iK)−2 R ψ(f ) .² :G;J;¾ HML@>T:C­®H@¾€O;KM<L>T:? ¦ ¹jKWJL?AH KK ¦ ¹;EAN3Q ¦M¦ E ¤ ? ¦ >PS=¹ ¦ 9LJ ¦œ[IUWdc[Ib*QðÇYIÊñòI ‡/FW‘“’j܇ó ͉ô@”ǏW‘!Ï@‰Œ’T— ’Y܇ó ˆGÍö‰dÎC‰Õ”Wó •M‰®óú‰è•˜—ϝŽ ”¥ˆŠ‰õÍFŽ#ß—ç” Í” Ï.ÐçænÓ Gˆ ͊ØFϐ"؉Œ—ç•Øz”®ˆŠ‰õÍFŽ–—ç”Ígα → δH = −i∇ + H0 + R∗ (eiK − 1)(iK)−1 A++ iR∗ (exp{iK} − iK − 1) (iK)−2 R,"óú‰Ù4é=jèÈÏ9àIŽ#Þ;‰M•˜—„Ï@‰ ”ÚǏŽ@•˜— Y”®ˆGÍö‰dÎC‰Õ‰Œ’T"ØzˆŠ”În󒊔qㆉ§•Œ—„Ï@”Ï@‰à —ç”͔ύAô” ÏM‰Œ„— Ï@” Í^ØYÙ4é HݒànÍFŽ@‰dϝ”Wó Ì|Ì •Õ”Ï–YÙ ÐWö®ÓÔÌ ÎC#Lε (H) áo*KâB H¹;ªJF­ª;?@9;HG_MH?@J©¹:´<L> ¦ ¹ ¦ KjXA9LHM_§H*>;:–­> ¦ Z:cN3Q ¦ _MH´HA< ¦ >;: ¤ HA>;:´¾ÀH¥S=½9LHnM? J? ¦ K ¤ J K ¤ HB©:K ¤ J;¨ ¦ K§GIH ¦ ¹ŠJL«#« ¦ > ¦ 9Lº;J;#: KjXA9LH ¦ EF>;:@?@9 ¦ 9;J ¦ OGIH ¤ H@>;H@¾/EH@9;Hç<LH¹Š¨LJ;9Fª ¦§¤ KÞª œ µ :@K§KM¾H ¤ >LJ;¾ <;> ¦ ¹ ¦ Klim ψ(w), U (t + dt) − U (t) ψ(v) ΓS = ψ(w), M (dt)ψ(v) ΓS ,t→+0¦ K ¤ HB©:K ¤ J;¨ ¦ K§G;J;¼*¹WJ;«#« ¦ > ¦ 9;ºLJT:K¦¦ 9 ­¥:?AJLK ¦Œ¤ XH ¤ ?GJ€LAH@>T:M (t) 9 ¹WHcKHS GIH@9;GL> ¦§¤ 9^JBGIHG_ ¦ > ¦ 9 ¤ 9HJB7? ¦ G ¤ HA>LHA? ψ(w) J ψ(v) œ ³ F< E“KMG©:Cª<;>;H@¾ ¦ SçE ¤ HA¨I½9HJ ¦ M? JGAKW:C¹WG;J`O­¥:<;JHZ ¦ ¾?GJ >;:#S ¦ 9LJ ¦ ¹^K;ª{K ¤ HBI:K ¤ J;¨ ¦ MK GIHG_MH¬¹WJ;«#« ¦ > ¦ 9©½ºLJT: KŠ: M (dt) ?ç«#H@>;¾ ¦ s*:C¹WKMH@9T: ¢\ :@> ¤ :@KM:@>;: ¤ J`Œ_â¹M (dt) = eiK − 1 dΛt+ eiK − 1 (iK)−1 iR dA†t + iR∗ eiK − 1 (iK)−1 dAt+ H0 + R∗ (eiK − iK − 1)(iK)−2 R dt.u KLª «#H@>;¾/EKWJL>;H@?AGLJ H@KM9;H@?@9;HG_MHl> ¦ ­MEKjX ¤ : ¤ :'< ¦ >L?AH@¼ _KW:@?GJhO?@? ¦ ¹Š»§¾?@KM<LHA¾HG_˜: ¤A¦ KjXA9LH ¦ <LHA9©ª ¤ J ¦ ³j¿F·n¶AµM÷‡·AøPÀW±^±F·²· ·¿FÀ¬¶`ÂÃc·n¶ò·¹n±YÂ!ø#±D·²· ù^·²ÀÁ¶`À±Ã¥±F·²·ú¸!ÀùÃc·n¶` ψ (J) œ\ H†HA<L> ¦ ¹ ¦ K ¦ 9;JHN;O¨a ¤ H†? ¦ G ¤ H@> «#H@GIH@?AK§GIHM_§H<L>;H@K ¤ >T:9;K ¤ ?A:HO‡anK ¦ ¾ ¦ 9 N¤ :@¾J^GIH ¤ HA>LHM_§HvªL?cKLª^N ¤ KÞª{H@< ¦ >;: ¤ H@>^J 9 ¦ GIH ¤ H@>;HG_MH§_ JAKYXGL ¦ > ¤ H@?“:=<L>;H@K ¤ >T:9;K ¤ ?A: H TO JL¾ ¦ N37Q J;¼Á?@J©¹‹Œ−ψN (H) = ←expZ†dx a (x)J(x) |0i,›®¡J ∈ L2 (B(H), R).<;H@>“ª©¹ŠH@¨ ¦ 9;J ¦ v? BL>LHA9LHcKTHM_§J;¨ ¦ KMGIH@¼paGIK§<;H@9 ¦ 9 ¤A¦ ? ¦ ¹W» ¤ KÞª~<LHi:>^_ŒEF¾ ¦ 9 ¤ :¾¦ ¤ >:œ ²¦ ¤¦ ¤x ∈ R HA< >T: HA;J(x) :@GLJ;¾ HGLA>;:–­HA¾€O4<;>;Jq¹ ¼LK ?AJLJGIH@¾À<LHA9 9 J¦¦ ¦ ¤φn(x1 .