Content-Type: multipart/mixed; boundary="-------------0609150940222" This is a multi-part message in MIME format. ---------------0609150940222 Content-Type: text/plain; name="06-261.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-261.keywords" time delay, scattering theory, classical scattering, S-matrix ---------------0609150940222 Content-Type: application/postscript; name="gen_delay.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="gen_delay.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: gen_delay.dvi %%Pages: 18 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: Times-Bold Times-Roman Times-Italic MSBM10 CMMI7 CMMI10 %%+ CMSY10 CMR10 CMR7 CMSS10 CMSY7 CMR5 CMEX10 CMMI5 TeX-cmex7 CMSY5 %%+ rsfs10 MSBM7 CMSS8 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o gen_delay.ps gen_delay.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2006.09.15:1501 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc 0 0 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 % % @@psencodingfile@{ % author = "S. 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readonly def /Copyright (Conversion from mf curves by Metafog (c) 1995 Richard Kinch) readonly def /Notice (Copyright (c) Taco Hoekwater, 1998. All rights reserved.) readonly def /FullName (rsfs10) readonly def /FamilyName (rsfs10) readonly def /ItalicAngle -12 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Roman) readonly def end readonly def /FontName /rsfs10 def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 66 /B put dup 70 /F put dup 85 /U put readonly def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /FontBBox {-2 -300 1240 728} readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 48 /prime put readonly def /FontBBox{21 -944 1448 791}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBAF552B11EFFB6A16C F03FB920C15AE724EFDF0CCBF00A838D34440FF9FED532F44036AD22561184C5 283722DDFA7285E62754372D716D704AC0E00B2F6AB67154241C7449AA047833 94CEDB08E8C92907FE72A0B05AE36A7B9226ACD6E7890A0B528FDDE84A950FC6 801DE75CF2E739E9121149CCB8B1C87A106822648D84A3D3FBF295EE6C4BF403 BBE9A1C1F6DAEDD1E642ACC486E609703D7612BFFD10C324F5DC710811F7F614 3691B400E3773987424C0D2B0D8A736873C6371DDB2442F05E018A2B5CA9A4AA 17AABB95D09E5890CFFFED5AC01495D89A53D3CEB6E0F620D2A75CB26E31E1FD 557B4C4A08F62668770C8BE63D101DB2855E6EE41C21A7EC6A61FAFC6ECC5AE3 AAAD9BF81CBE3446C7B97DF168DA97FD62D7624466B71DEC005100D9A9E96639 5D681ABD5C673876B65E5CCBA7EDC02360AAC47245CDEEF83F773B666AD6DC02 D2BD2B915D7F5BFE8B348B2ABFC170B60903A197F9D7F0452749B5B45CCA8A89 767A0CBA59727444D2E23EEDC51BCDF62C922C96FC225D37C55536A490E40274 A36DF874CE42AF66263960453C382B40F572B09FACE25BA9023E411D3FAF92E4 AE4859DC5A7D9CE12B95F62B662E5531F8A37684975192DF23B55CFBB20BB4E5 B18717E883CF36296D11F1B58CCF4D03CC1876247CC4D1CC3BFE1A4041071ECB D77CD059296E3626A1ACD84A974F0D211B495656343D2E85743F89563F194070 A699C86C5F1A47549F2802834AC91878C6240B7E2663C5EBAED531493794BF23 E6F9892376F2C74804F91073B53A444B0987184AADD149F0C489CD0E26859A29 8053B9756F60A4BEE5A5339AEDCCA27AF48BCDEC28208A5DD74F85B397E5BBDA 3B9CDB74B0ED57B6CCAF77891D15EA90D4D8A4FD6F446C1643D84732F60DE890 B162DCE64321E5551F28A11A3E 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: TeX-cmex7 %!PS-AdobeFont-1.0: TeX-cmex7 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex7) def /FullName (TeX\040cmex7\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put readonly def /FontBBox {-14 -2954 1627 771} readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /mu put dup 23 /nu put dup 100 /d put dup 114 /r put readonly def /FontBBox{37 -250 1349 750}readonly def currentdict end currentfile eexec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%%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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%%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 21 /greaterequal put dup 33 /arrowright put dup 38 /arrowsoutheast put dup 49 /infinity put dup 50 /element put dup 66 /B put dup 106 /bar put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 76 /L put readonly def /FontBBox{-61 -250 999 759}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 6 /Sigma put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 61 /equal put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 6 /Sigma put dup 8 /Phi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 58 /colon put dup 61 /equal put dup 67 /C put dup 91 /bracketleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 6 /plusminus put dup 7 /minusplus put dup 14 /openbullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 66 /B put dup 68 /D put dup 69 /E put dup 72 /H put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put dup 114 /nabla 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 27 /sigma put dup 28 /tau put dup 31 /chi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 74 /J put dup 75 /K put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 90 /Z put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 100 /d put dup 102 /f put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 72 /H put dup 74 /J put dup 80 /P put dup 81 /Q put dup 83 /S put dup 90 /Z put dup 96 /lscript put dup 97 /a put dup 100 /d put dup 105 /i put dup 114 /r put dup 115 /s put dup 116 /t put dup 120 /x put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 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a Fv(W)-7 b(e)32 b(adapt)e(our)g (approach)f(from)h([9)o(,)h(Sec.)g(2].)g(In)f(particular)g(we)h (suppose)f(in)h(the)g(rest)g(of)515 623 y(the)f(section)h(that)f Fq(\006)1129 635 y Ft(r)1208 623 y Fq(:=)42 b Fr(f)p Fs(r)r(x)h Fr(j)f Fs(x)h Fr(2)g Fq(\006)p Fr(g)p Fv(,)30 b(where)g Fq(\006)h Fv(is)g(a)g(con)m(v)o(e)o(x)d(bounded)g(open)i(set) h(\(with)515 722 y(smooth)16 b(boundary\))f(in)j Fu(R)1280 692 y Ft(d)1336 722 y Fv(containing)e Fq(0)p Fv(.)h(Let)h Fs(V)37 b Fv(be)18 b(a)g(real)g Fs(C)2359 692 y Fp(2)2396 722 y Fv(-potential)e(with)i(compact)f(support.)515 822 y(A)31 b Fj(scattering)f(tr)o(ajectory)h Fv(for)f Fs(V)50 b Fv(is)32 b(a)f(map)f Fq(\010)43 b(:)f Fu(R)h Fr(3)g Fs(t)g Fr(7!)f Fq(\()p Fs(x)p Fq(\()p Fs(t)p Fq(\))p Fs(;)14 b(p)p Fq(\()p Fs(t)p Fq(\)\))45 b Fr(2)d Fu(R)3029 792 y Ft(d)3099 822 y Fv(solution)30 b(of)529 922 y Fq(_)-37 b Fs(x)p Fq(\()p Fs(t)p Fq(\))25 b(=)f Fs(p)p Fq(\()p Fs(t)p Fq(\))p Fv(,)37 b Fq(_)-39 b Fs(p)p Fq(\()p Fs(t)p Fq(\))24 b(=)g Fr(\000r)p 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Ft(r)1870 4744 y Fr(\000)1963 4711 y Fp(1)p 1963 4725 34 4 v 1963 4772 a(2)2006 4677 y Fl(\000)2044 4744 y Fs(T)2105 4710 y Fp(0)2093 4764 y Ft(r)2159 4744 y Fq(+)18 b Fs(T)2303 4710 y Fp(0)2336 4685 y Fg(0)2291 4764 y Ft(r)2362 4677 y Fl(\001)2400 4744 y Fs(:)885 b Fv(\(3.6\))1970 5059 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 515 523 a Fi(Remark)34 b(3.1.)49 b Fj(Let)35 b Fq(\010)49 b(:)g Fu(R)f Fr(3)h Fs(t)g Fr(7!)g Fq(\()p Fs(x)p Fq(\()p Fs(t)p Fq(\))p Fs(;)14 b(p)p Fq(\()p Fs(t)p Fq(\)\))51 b Fr(2)e Fu(R)2353 493 y Ft(d)2426 523 y Fj(be)34 b(a)g(scattering)g(tr)o(ajectory)g(and)515 623 y Fs(p)557 635 y Fn(\006)659 623 y Fr(\021)45 b Fs(p)811 635 y Fn(\006)867 623 y Fq(\(\010\))p Fj(,)34 b Fs(t)1076 635 y Fn(\006)1178 623 y Fr(\021)46 b Fs(t)1319 635 y Fn(\006)1375 623 y Fq(\(\010\))p Fj(,)33 b Fs(x)1600 635 y Fn(\006)1703 623 y Fr(\021)45 b Fs(x)1860 635 y Fn(\006)1917 623 y Fq(\(\010\))p Fj(,)36 b Fl(e)-49 b Fs(x)2142 635 y Fn(\006)2245 623 y Fr(\021)49 b Fl(e)-49 b 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Fv(\(see)g([11)o(,)f(Sec.)g(2.1]\))743 2697 y Fs(\034)788 2662 y Fp(free)779 2717 y Ft(r)898 2697 y Fq(\()p Fs(')p Fq(\))k(:=)1161 2664 y Fp(1)p 1161 2678 V 1161 2725 a(2)1217 2584 y Fl(Z)1300 2604 y Fp(0)1264 2772 y Fn(\0001)1400 2697 y Fq(d)p Fs(t)1490 2629 y Fl(\000)1528 2697 y Fr(k)p Fs(\037)1622 2709 y Ft(r)1658 2697 y Fq(\()p Fs(Q)p Fq(\))1802 2694 y(e)1839 2662 y Fn(\000)p Fp(i)p Ft(tH)1989 2670 y Fm(0)2039 2697 y Fs(')p Fr(k)2135 2662 y Fp(2)2191 2697 y Fr(\000)18 b(k)p Fs(\037)2368 2709 y Ft(r)2404 2697 y Fq(\()p Fs(Q)p Fq(\))2548 2694 y(e)2585 2662 y Fn(\000)p Fp(i)p Ft(tH)2735 2670 y Fm(0)2786 2697 y Fs(S)5 b(')p Fr(k)2938 2662 y Fp(2)2974 2629 y Fl(\001)3267 2697 y Fv(\(4.12\))1222 2941 y Fq(+)1315 2908 y Fp(1)p 1315 2922 V 1315 2970 a(2)1372 2828 y Fl(Z)1455 2848 y Fp(+)p Fn(1)1418 3017 y Fp(0)1590 2941 y Fq(d)p Fs(t)1680 2874 y Fl(\000)1718 2941 y Fr(k)p Fs(\037)1812 2953 y Ft(r)1848 2941 y Fq(\()p Fs(Q)p Fq(\))1992 2938 y(e)2029 2907 y Fn(\000)p Fp(i)p Ft(tH)2179 2915 y 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Fn(\000)p Fp(i)p Ft(tH)1645 4398 y Fm(0)1695 4424 y Fs(')1749 4354 y Fl(\015)1749 4403 y(\015)1893 4424 y Fv(and)82 b Fs(f)2137 4436 y Fp(+)2191 4424 y Fq(\()p Fs(t)p Fq(\))24 b(:=)2420 4354 y Fl(\015)2420 4403 y(\015)2466 4421 y Fq(e)2503 4390 y Fn(\000)p Fp(i)p Ft(tH)2675 4424 y Fs(W)2765 4390 y Fp(+)2820 4424 y Fs(')19 b Fr(\000)2976 4421 y Fq(e)3013 4390 y Fn(\000)p Fp(i)p Ft(tH)3163 4398 y Fm(0)3214 4424 y Fs(S)5 b(')3324 4354 y Fl(\015)3324 4403 y(\015)3384 4424 y Fs(:)515 4607 y Fv(W)-7 b(e)21 b(kno)n(w)e(from)g(Hypotheses)h(\(4.13\))e(and)h(\(4.14\))g(that)h Fs(f)2207 4619 y Fn(\006)2286 4607 y Fr(2)j Fo(L)2401 4577 y Fp(1)2439 4607 y Fq(\()p Fu(R)2531 4619 y Fn(\006)2587 4607 y Fq(\))p Fv(.)e(Using)f(the)g(inequality)1121 4719 y Fl(\014)1121 4769 y(\014)1149 4790 y Fr(k)p Fs(u)p Fr(k)1281 4755 y Fp(2)1335 4790 y Fr(\000)e(k)p Fs(v)s Fr(k)1545 4755 y Fp(2)1582 4719 y Fl(\014)1582 4769 y(\014)1632 4790 y Fr(\024)23 b(k)p Fs(u)17 b Fr(\000)h Fs(v)s Fr(k)p Fq(\()p Fr(k)p Fs(u)p Fr(k)f Fq(+)i Fr(k)p Fs(v)s Fr(k)p Fq(\))p Fs(;)96 b(u;)14 b(v)26 b Fr(2)d(H)q Fs(;)406 b Fv(\(4.15\))1970 5059 y(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 515 523 a Fv(we)20 b(obtain)g(the)g(estimates)985 626 y Fl(\014)985 676 y(\014)1013 697 y Fr(k)p Fs(\037)1107 709 y Ft(r)1143 697 y Fq(\()p Fs(Q)p Fq(\))1287 694 y(e)1324 662 y Fn(\000)p Fp(i)p Ft(tH)1496 697 y Fs(W)1586 662 y Fn(\000)1642 697 y Fs(')p Fr(k)1738 662 y Fp(2)1794 697 y Fr(\000)e(k)p Fs(\037)1971 709 y Ft(r)2007 697 y Fq(\()p Fs(Q)p Fq(\))2151 694 y(e)2188 662 y Fn(\000)p Fp(i)p Ft(tH)2338 670 y Fm(0)2388 697 y Fs(')p Fr(k)2484 662 y Fp(2)2522 626 y Fl(\014)2522 676 y(\014)2572 697 y Fr(\024)23 b Fq(2)p Fs(f)2743 709 y Fn(\000)2798 697 y Fq(\()p Fs(t)p Fq(\))p Fr(k)p Fs(')p Fr(k)p Fs(;)929 763 y Fl(\014)929 813 y(\014)957 834 y Fr(k)p Fs(\037)1051 846 y Ft(r)1087 834 y Fq(\()p Fs(Q)p Fq(\))1231 831 y(e)1268 799 y Fn(\000)p Fp(i)p Ft(tH)1441 834 y Fs(W)1531 799 y Fn(\000)1587 834 y Fs(')p Fr(k)1683 799 y Fp(2)1738 834 y Fr(\000)18 b(k)p Fs(\037)1915 846 y Ft(r)1951 834 y Fq(\()p Fs(Q)p Fq(\))2095 831 y(e)2132 799 y Fn(\000)p Fp(i)p Ft(tH)2282 807 y Fm(0)2333 834 y Fs(S)5 b(')p Fr(k)2485 799 y Fp(2)2522 763 y Fl(\014)2522 813 y(\014)2572 834 y Fr(\024)23 b Fq(2)p Fs(f)2743 846 y Fp(+)2797 834 y Fq(\()p Fs(t)p Fq(\))p Fr(k)p Fs(')p Fr(k)p Fs(:)515 1007 y Fv(Since)34 b(s-)14 b Fq(lim)923 1019 y Ft(r)r Fn(!)p Fp(+)p Fn(1)1157 1007 y Fs(\037)1209 1019 y Ft(r)1245 1007 y Fq(\()p Fs(Q)p Fq(\))49 b(=)f(1)-18 b(l)p Fv(,)34 b(then)f(the)h(scalars)h(on)e(the)h(l.h.s.)g(abo)o(v)o(e)e(con)m(v)o (er)o(ge)f(to)j Fq(0)g Fv(as)515 1107 y Fs(r)k Fr(!)d Fq(+)p Fr(1)p Fv(.)27 b(Thus)f(the)h(claim)f(follo)n(ws)h(from)e (\(4.12\))g(and)h(Lebesgue')-5 b(s)26 b(dominated)f(con)m(v)o(er)o (gence)515 1207 y(theorem.)p 3407 1207 4 57 v 3411 1154 50 4 v 3411 1207 V 3460 1207 4 57 v 515 1443 a Ff(4.2)99 b(T)n(ime)25 b(r)n(e)o(v)o(ersal)515 1598 y Fv(W)-7 b(e)20 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Fn(\007)2803 2502 y Fs(')d Fv(and)1781 2675 y Fs(S)p 1837 2630 55 4 v 5 w(')i Fq(=)p 2002 2604 200 4 v 23 w Fs(S)2058 2651 y Fn(\000)p Fp(1)2147 2675 y Fs(')1066 b Fv(\(4.16\))515 2849 y(for)19 b(each)h Fs(')k Fr(2)f(H)q Fv(.)d(Consider)g(the)g (bijection)1590 3023 y Fq(f)k(:)f Fr(H)h(!)f(H)q Fs(;)97 b(')23 b Fr(7!)p 2259 2956 111 4 v 23 w Fs(S)5 b(';)515 3196 y Fv(which)20 b(we)i(call)f Fj(full)g(time)h(r)m(e)o(ver)o(sal)p Fv(.)f(The)g(map)f Fq(f)28 b Fv(corresponds)19 b(to)i(time)g(re)n(v)o (ersal)f(for)h(the)g Fj(full)g(scat-)515 3296 y(tering)16 b(pr)l(ocess)p Fv(,)h Fj(i.e)o(.)f Fv(it)h(interchanges)d(past)j(and)f (future)f(scattering)g(data)i(and)e(re)n(v)o(erses)h(the)g(direction) 515 3396 y(of)k(time.)g(Furthermore)e(one)h(sees)i(easily)g(from)e (\(4.16\))f(that)i Fq(f)28 b Fv(is)21 b(an)f(antiunitary)f(in)m(v)n (olution.)704 3495 y(In)30 b(order)g(to)h(gi)n(v)o(e)f(a)i(rigourous)c (interpretation)h(of)i(full)g(time)g(re)n(v)o(ersal)f(we)h(introduce)e (the)515 3595 y(space)20 b 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Fv(de\002ned)d(by)h(the)h(constraint)1383 4810 y(s-)d Fq(lim)1572 4822 y Ft(t)p Fn(!\0001)1800 4743 y Fl(\000)1838 4810 y Fq(\010\()p Fs(t)p Fq(\))19 b Fr(\000)2094 4807 y Fq(e)2131 4776 y Fn(\000)p Fp(i)p Ft(tH)2281 4784 y Fm(0)2331 4810 y Fs(')2385 4743 y Fl(\001)2447 4810 y Fq(=)j(0)p Fs(:)1970 5059 y Fv(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 515 523 a Fv(Due)20 b(to)g(the)g(completeness)e (of)i(the)g(w)o(a)n(v)o(e)g(operators)f(we)h(kno)n(w)f(that)h Fs(T)34 b Fq(:)23 b Fr(E)30 b(!)23 b(H)f Fv(is)f(bijecti)n(v)o(e,)e (and)515 623 y(we)h(ha)n(v)o(e)1445 722 y Fq(f\()p Fs(')p Fq(\))k(=)1700 655 y Fl(\000)1738 722 y Fs(T)12 b(R)q(T)1924 688 y Fn(\000)p Fp(1)2011 655 y Fl(\001)2049 722 y Fq(\()p Fs(')p Fq(\))p Fs(;)98 b(')23 b Fr(2)g(H)q Fs(:)730 b Fv(\(4.17\))515 853 y(Equation)16 b(\(4.17\))f(pro)o(vides)h(a)i (rigourous)d(meaning)h(to)i(full)f(time)g(re)n(v)o(ersal)g(as)h(a)g (map)f(interchanging)515 952 y(past)j(and)g(future)f(scattering)g(data) 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y(Thus)27 b Fs(\034)934 1709 y Ft(r)971 1697 y Fq(\()p Fs(')p Fq(\))i Fv(is)f(the)g(mean)f(v)n(alue)g (of)g(the)h(usual)f(time)h(delay)f Fs(\034)2604 1667 y Fp(in)2595 1718 y Ft(r)2664 1697 y Fq(\()p Fs(')p Fq(\))i Fv(and)e(of)g(the)h(time)f(de-)515 1797 y(lay)d Fs(\034)686 1767 y Fp(out)677 1818 y Ft(r)786 1797 y Fq(\()p Fs(')p Fq(\))h Fv(corresponding)c(to)j(the)g(time)g(re)n(v)o(ersed)e (scattering)h(process.)h(In)f(particular)g Fs(\034)3232 1809 y Ft(r)3269 1797 y Fq(\()p Fs(')p Fq(\))i Fv(is)515 1897 y(in)m(v)n(ariant)18 b(under)h(full)h(time)g(re)n(v)o(ersal.)515 2056 y Fj(Pr)l(oof.)40 b Fv(Since)21 b Fs(H)1037 2068 y Fp(0)1095 2056 y Fv(is)g(in)m(v)n(ariant)d(under)h(time)h(re)n(v)o (ersal,)f(one)h(gets)1708 2207 y Fs(T)1769 2173 y Fp(0)1757 2228 y Ft(r)1805 2207 y Fq(\()p Fs(')p Fq(\))k(=)f Fs(T)2096 2173 y Fp(0)2084 2228 y Ft(r)2132 2207 y Fq(\()p 2164 2162 55 4 v Fs(')q Fq(\))p Fs(:)515 2359 y Fv(This)d(together)f(with)h (time)h(re)n(v)o(ersal)e(in)m(v)n(ariance)f(of)i Fs(H)27 b Fv(yields)1692 2510 y Fs(T)1741 2522 y Ft(r)1778 2510 y Fq(\()p 1810 2443 111 4 v Fs(S)5 b(')p Fq(\))23 b(=)g Fs(T)2112 2522 y Ft(r)2148 2510 y Fq(\()p Fs(')p Fq(\))p Fs(:)515 2661 y Fv(Thus)936 2760 y Fs(\034)981 2726 y Fp(out)972 2781 y Ft(r)1082 2760 y Fq(\()p Fs(')p Fq(\))h(=)e Fs(\034)1356 2726 y Fp(in)1347 2781 y Ft(r)1416 2760 y Fq(\()p 1448 2694 V Fs(S)5 b(')q Fq(\))23 b(=)g Fs(T)1751 2772 y Ft(r)1787 2760 y Fq(\()p 1819 2694 V Fs(S)5 b(')p Fq(\))19 b Fr(\000)f Fs(T)2124 2726 y Fp(0)2112 2781 y Ft(r)2160 2760 y Fq(\()p 2192 2694 V Fs(S)5 b(')q Fq(\))23 b(=)g Fs(T)2495 2772 y Ft(r)2531 2760 y Fq(\()p Fs(')p Fq(\))c(+)f Fs(T)2812 2726 y Fp(0)2800 2781 y Ft(r)2849 2760 y Fq(\()p Fs(S)5 b(')p Fq(\))p Fs(;)515 2891 y Fv(which)21 b(implies)g(the)h(\002rst)g(identity)f(in)h(\(4.18\))m(.)g(The)g (second)e(identity)h(follo)n(ws)g(from)g(the)g(f)o(act)h(that)g Fq(f)515 2990 y Fv(is)f(an)f(in)m(v)n(olution.)p 3407 2990 4 57 v 3411 2938 50 4 v 3411 2990 V 3460 2990 4 57 v 515 3222 a Ff(4.3)99 b(T)n(ime)25 b(delay)515 3378 y Fv(In)h(the)h(present)f(section)g(we)h(shall)g(gi)n(v)o(e)f(the)g (proof)f(of)i(the)f(e)o(xistence)g(of)g(the)h(symmetrized)e(time)515 3478 y(delay)-5 b(.)25 b(W)-7 b(e)28 b(\002rst)f(\002x)g(some)g (notation.)e(If)h Fs(A;)14 b(B)32 b Fv(are)26 b(tw)o(o)h(symmetric)f (operators,)f(then)h(we)h(set)h(for)515 3577 y(each)20 b Fs(')j Fr(2)g(D)r Fq(\()p Fs(A)p Fq(\))d Fr(\\)f(D)r Fq(\()p Fs(B)t Fq(\))p Fv(:)1304 3728 y Fq(\()q Fs(';)14 b Fq([)p Fs(A;)g(B)t Fq(])p Fs(')p Fq(\))24 b(:=)f(\()p Fs(A';)14 b(B)t(')p Fq(\))20 b Fr(\000)e Fq(\()p Fs(B)t(';)c(A')p Fq(\))h Fs(:)515 3879 y Fv(If)27 b Fs(q)j Fv(is)f(a)e(quadratic)f(form) g(with)h(domain)f Fr(D)r Fq(\()p Fs(q)s Fq(\))p Fv(,)i(and)f Fs(S)32 b Fv(is)c(unitary)-5 b(,)26 b(then)g(we)i(set)g(for)e(each)h Fs(')36 b Fr(2)515 3979 y(D)r Fq(\()p Fs(q)s Fq(\))19 b Fr(\\)g Fs(S)834 3949 y Fn(\000)p Fp(1)923 3979 y Fr(D)r Fq(\()p Fs(q)s Fq(\))p Fv(:)1434 4079 y Fq(\()p Fs(';)14 b(S)1613 4044 y Fn(\003)1651 4079 y Fq([)p Fs(q)s(;)g(S)5 b Fq(])p Fs(')p Fq(\))24 b(:=)e Fs(q)s Fq(\()p Fs(S)5 b(')p Fq(\))19 b Fr(\000)f Fs(q)s Fq(\()p Fs(')p Fq(\))p Fs(:)515 4209 y Fv(If)32 b Fs(A)i Fv(is)g(an)e(operator)f(with)i (domain)e Fr(D)r Fq(\()p Fs(A)p Fq(\))k Fv(and)d Fs(S)38 b Fv(is)c(unitary)-5 b(,)31 b(then)h(we)h(de\002ne)f(the)h(operator)515 4309 y Fs(S)571 4279 y Fn(\003)609 4309 y Fq([)p Fs(A;)14 b(S)5 b Fq(])20 b Fv(with)h(domain)e Fr(D)r Fq(\()p Fs(A)p Fq(\))g Fr(\\)g Fs(S)1610 4279 y Fn(\000)p Fp(1)1699 4309 y Fr(D)r Fq(\()p Fs(A)p Fq(\))j Fv(by)1578 4460 y Fs(S)1634 4426 y Fn(\003)1671 4460 y Fq([)p Fs(A;)14 b(S)5 b Fq(])23 b(:=)g Fs(S)2062 4426 y Fn(\003)2100 4460 y Fs(AS)g Fr(\000)18 b Fs(A:)515 4611 y Fv(W)-7 b(e)22 b(also)f(recall)g(that)g(the)g(function)e Fs(G)1638 4623 y Fp(\006)1711 4611 y Fv(w)o(as)j(introduced)d(in)i(Section)f(2)h (and)g(that)g Fr(D)3009 4623 y Fp(2)3070 4611 y Fr(\032)j(D)r Fq(\()p Fs(Q)3323 4581 y Fp(2)3361 4611 y Fq(\))19 b Fr(\\)515 4710 y(D)r Fq(\()p Fs(G)678 4722 y Fp(\006)730 4710 y Fq(\()p Fs(P)12 b Fq(\)\))p Fv(.)21 b(Therefore)d(the)j (quadratic)d(form)h Fq(i[)p Fs(Q)2027 4680 y Fp(2)2064 4710 y Fs(;)14 b(G)2166 4722 y Fp(\006)2218 4710 y Fq(\()p Fs(P)e Fq(\)])21 b Fv(is)h(well)e(de\002ned)f(on)h Fr(D)3064 4722 y Fp(2)3101 4710 y Fv(.)704 4810 y(The)g(proof)e(of)i(the)g(ne)o (xt)g(proposition)e(can)i(be)g(found)e(in)j(the)f(appendix.)1950 5059 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 515 523 a Fi(Pr)o(oposition)22 b(4.5.)42 b Fj(Let)24 b Fq(\006)g Fj(satisfy)g(Assumption)e(2.1.)h (Suppose)e(that)i(Assumption)g(4.1)f(is)j(veri\002ed.)515 623 y(Then)20 b(we)h(have)e(for)i(all)f Fs(')j Fr(2)h(D)1438 635 y Fp(2)1496 623 y Fj(the)c(equality)801 860 y Fq(lim)750 909 y Ft(r)r Fn(!)p Fp(+)p Fn(1)980 747 y Fl(Z)1063 767 y Fp(+)p Fn(1)1026 935 y Fp(0)1198 860 y Fq(d)p Fs(t)1288 792 y Fl(\000)1326 860 y Fs(';)1417 792 y Fl(\000)1470 857 y Fq(e)1506 825 y Fp(i)p Ft(tP)1601 800 y Fm(2)1634 825 y Ft(=)p Fp(2)1719 860 y Fs(\037)1771 872 y Ft(r)1808 860 y Fq(\()p Fs(Q)p Fq(\))1952 857 y(e)1989 825 y Fn(\000)p Fp(i)p Ft(tP)2136 800 y Fm(2)2168 825 y Ft(=)p Fp(2)2253 860 y Fr(\000)2332 857 y Fq(e)2368 825 y Fn(\000)p Fp(i)p Ft(tP)2515 800 y Fm(2)2548 825 y Ft(=)p Fp(2)2633 860 y Fs(\037)2685 872 y Ft(r)2722 860 y Fq(\()p Fs(Q)p Fq(\))2866 857 y(e)2903 825 y Fp(i)p Ft(tP)2998 800 y Fm(2)3030 825 y Ft(=)p Fp(2)3115 792 y Fl(\001)3153 860 y Fs(')3207 792 y Fl(\001)760 1040 y Fq(=)i Fr(\000)926 973 y Fl(\000)964 1040 y Fs(';)14 b Fq(i[)p Fs(Q)1167 1006 y Fp(2)1204 1040 y Fs(;)g(G)1306 1052 y Fp(\006)1358 1040 y Fq(\()p Fs(P)e Fq(\)])p Fs(')1564 973 y Fl(\001)1616 1040 y Fs(:)1628 b Fv(\(4.19\))704 1223 y(W)-7 b(e)31 b(are)f(no)n(w)g(in)g(a)h (position)e(to)i(gi)n(v)o(e)e(the)h(proof)f(of)h(our)f(main)h(theorem.) f(It)h(in)m(v)n(olv)o(es)f(the)515 1322 y(operator)1519 1422 y Fs(A)1581 1434 y Fp(0)1641 1422 y Fq(:=)1762 1389 y Fp(1)p 1762 1403 34 4 v 1762 1451 a(2)1805 1355 y Fl(\000)1869 1389 y Ft(P)p 1853 1403 84 4 v 1853 1451 a(P)1904 1434 y Fm(2)1965 1422 y Fr(\001)18 b Fs(Q)g Fq(+)g Fs(Q)h Fr(\001)2325 1389 y Ft(P)p 2309 1403 V 2309 1451 a(P)2360 1434 y Fm(2)2403 1355 y Fl(\001)2441 1422 y Fs(;)515 1572 y Fv(which)g(is)j(well-de\002ned)c(and)i(symmetric)f(on)h Fr(D)1930 1584 y Fp(1)1967 1572 y Fv(.)515 1738 y Fi(Theor)o(em)g(4.6.) 39 b Fj(Let)21 b Fq(\006)g Fj(satisfy)f(Assumption)f(2.1.)h(Suppose)e (that)i(Assumption)f(4.1)g(is)i(veri\002ed.)e(Let)515 1837 y Fs(')36 b Fr(2)g(D)760 1849 y Fp(2)825 1837 y Fj(satisfy)28 b Fv(\(4.13\))m Fj(,)g Fv(\(4.14\))d Fj(and)h Fs(S)5 b(')36 b Fr(2)g(D)1995 1849 y Fp(2)2032 1837 y Fj(.)28 b(Then)e(the)i(limit)f Fs(\034)2619 1849 y Fp(\006)2671 1837 y Fq(\()p Fs(')p Fq(\))37 b(=)e(lim)3042 1849 y Ft(r)r Fn(!)p Fp(+)p Fn(1)3276 1837 y Fs(\034)3312 1849 y Ft(r)3349 1837 y Fq(\()p Fs(')p Fq(\))515 1937 y Fj(e)n(xists,)21 b(and)e(one)h(has)927 2119 y Fs(\034)963 2131 y Fp(\006)1015 2119 y Fq(\()p Fs(')p Fq(\))k(=)e Fr(\000)1319 2087 y Fp(1)p 1319 2101 34 4 v 1319 2148 a(2)1362 2052 y Fl(\000)1400 2119 y Fs(';)14 b(S)1547 2089 y Fn(\003)1585 2052 y Fl(\002)1620 2119 y Fq(i)1643 2052 y Fl(\002)1677 2119 y Fs(Q)1743 2089 y Fp(2)1780 2119 y Fs(;)g(G)1882 2131 y Fp(\006)1934 2052 y Fl(\000)2002 2087 y Ft(P)p 1982 2101 91 4 v 1982 2148 a Fn(j)p Ft(P)9 b Fn(j)2083 2052 y Fl(\001\003)2155 2119 y Fs(;)14 b(S)2248 2052 y Fl(\003)2282 2119 y Fs(')2336 2052 y Fl(\001)2393 2119 y Fr(\000)k Fq(\()p Fs(';)c(S)2655 2089 y Fn(\003)2694 2119 y Fq([)p Fs(A)2779 2131 y Fp(0)2816 2119 y Fs(;)g(S)5 b Fq(])p Fs(')p Fq(\))14 b Fs(:)212 b Fv(\(4.20\))704 2326 y(The)22 b(quadratic)f(form)g Fq(i[)p Fs(Q)1484 2296 y Fp(2)1521 2326 y Fs(;)14 b(G)1623 2338 y Fp(\006)1675 2326 y Fq(\()1737 2294 y Ft(P)p 1717 2308 V 1717 2355 a Fn(j)p Ft(P)9 b Fn(j)1818 2326 y Fq(\)])23 b Fv(and)f(the)g(operator)f Fs(A)2525 2338 y Fp(0)2585 2326 y Fv(are)h(well)h(de\002ned)f(on)g Fr(D)3313 2338 y Fp(2)3350 2326 y Fv(,)h(so)515 2435 y(all)e(the)f(commutators)e(in)i 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b(ormula)25 b Fv(\(4.21\))e Fj(is)i(clearly)g(co)o (variant)f(under)515 1831 y(spatial)c(tr)o(anslations.)515 2067 y Ff(4.4)99 b(Stationary)25 b(f)n(ormulas)515 2222 y Fv(In)f(the)g(sequel)g(we)g(suppose)g(that)g Fq(\006)h Fv(satisfy)f(Assumption)f(2.1.)h(W)-7 b(e)25 b(kno)n(w)e(from)g(Remark) h(2.3.\(c\))515 2322 y(that)c(there)g(e)o(xists)g(a)h(symmetric)e(star) n(-shaped)g(set)2001 2301 y Fl(e)1994 2322 y Fq(\006)i Fv(such)f(that)1708 2513 y Fs(\034)1753 2479 y Fp(\006)1805 2513 y Fq(\()p Fs(')p Fq(\))k(=)f Fs(\034)2086 2464 y Fh(e)2080 2479 y Fp(\006)2132 2513 y Fq(\()p Fs(')p Fq(\))p Fs(;)515 2686 y Fv(for)f Fs(')h Fv(satisfying)f(the)h(hypotheses)e(of)h (Theorem)f(4.6.)h(Thus)g(with)h(no)f(loss)i(of)e(generality)f(we)j(may) 515 2786 y(assume)j(that)h Fq(\006)h Fv(is)f(symmetric)f(and)g(star)n (-shaped.)g(W)-7 b(e)29 b(also)f(assume)g(that)g(the)f(boundary)e Fs(@)5 b Fq(\006)28 b Fv(of)515 2886 y Fq(\006)d Fv(is)h(a)f Fs(C)808 2856 y Fp(2)871 2886 y 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Fl(\001)2694 3159 y Fr(\001)19 b Fs(Q)2802 3091 y Fl(\003)2859 3159 y Fq(=:)k Fs(B)3033 3171 y Fp(\006)3084 3159 y Fs(;)515 3341 y Fv(as)30 b(quadratic)e(forms)g(on)i Fr(D)1354 3353 y Fp(2)1421 3341 y Fv(\(note)e(that)i Fs(B)1839 3353 y Fp(\006)1920 3341 y Fv(is)h(a)f(well-de\002ned)e (symmetric)g(operator)g(on)h Fr(D)3382 3353 y Fp(1)3419 3341 y Fv(\).)515 3440 y(Thus)20 b(we)g(can)g(re)n(write)g Fs(\034)1254 3410 y Fp(\006)1306 3440 y Fq(\()p Fs(')p Fq(\))i Fv(as)1174 3614 y Fs(\034)1210 3626 y Fp(\006)1262 3614 y Fq(\()p Fs(')p Fq(\))i(=)f Fr(\000)14 b Fq(\()o Fs(';)g(S)1749 3579 y Fn(\003)1788 3614 y Fq([)p Fs(B)1874 3626 y Fp(\006)1925 3614 y Fs(;)g(S)5 b Fq(])p Fs(')p Fq(\))19 b Fr(\000)f Fq(\()p Fs(';)c(S)2408 3579 y Fn(\003)2446 3614 y Fq([)p Fs(A)2531 3626 y Fp(0)2569 3614 y Fs(;)g(S)5 b Fq(])p Fs(')p Fq(\))14 b Fs(:)459 b Fv(\(4.22\))515 3799 y(Let)16 b Fe(U)45 b Fq(:)23 b Fo(L)836 3769 y Fp(2)874 3799 y Fq(\()p Fu(R)966 3769 y Ft(d)1005 3799 y Fq(\))g Fr(!)1166 3732 y Fl(R)1222 3752 y Fn(\010)1205 3828 y Fd(R)1247 3836 y Fm(+)1312 3799 y Fq(d)p Fs(\025)14 b Fo(L)1457 3769 y Fp(2)1495 3799 y Fq(\()p Fu(S)1573 3769 y Ft(d)p Fn(\000)p Fp(1)1697 3799 y Fq(\))j Fv(be)f(the)h(spectral)e (transformation)f(for)h Fs(H)2922 3811 y Fp(0)2960 3799 y Fv(,)h Fj(i.e)o(.)g Fv(the)g(unitary)515 3908 y(mapping)i(de\002ned)h (by)1279 4082 y Fq(\()p Fe(U)j Fs(')p Fq(\)\()p Fs(\025;)14 b(!)s Fq(\))24 b(=)f(\(2)p Fs(\025)p Fq(\))1955 4048 y Fp(\()p Ft(d)p Fn(\000)p Fp(2\))p Ft(=)p Fp(4)2198 4082 y Fq(\()p Fe(F)11 b Fs(')p Fq(\)\()2433 4007 y Fr(p)p 2504 4007 90 4 v 2504 4082 a Fq(2)p Fs(\025!)s Fq(\))p Fs(;)515 4255 y Fv(where)19 b Fe(F)33 b Fv(denotes)19 b(the)h(F)o(ourier)f(transform.)g(One)h(has)1003 4467 y Fe(U)i Fs(H)1160 4479 y Fp(0)1197 4467 y Fe(U)1285 4433 y Fn(\000)p Fp(1)1397 4467 y Fq(=)1485 4354 y Fl(Z)1568 4374 y Fn(\010)1531 4543 y Fd(R)1573 4551 y Fm(+)1638 4467 y Fq(d)p Fs(\025)14 b(\025)84 b Fq(and)f Fe(U)21 b Fs(S)5 b Fe(U)2326 4433 y Fn(\000)p Fp(1)2438 4467 y Fq(=)2526 4354 y Fl(Z)2609 4374 y Fn(\010)2572 4543 y Fd(R)2614 4551 y Fm(+)2679 4467 y Fq(d)p Fs(\025)14 b(S)5 b Fq(\()p Fs(\025)p Fq(\))p Fs(;)515 4710 y Fv(where)29 b Fr(f)p Fs(S)5 b Fq(\()p Fs(\025)p Fq(\))p Fr(g)1000 4722 y Ft(\025)p Fn(\025)p Fp(0)1168 4710 y Fr(\032)40 b Fe(B)1351 4643 y Fl(\000)1390 4710 y Fo(L)1427 4680 y Fp(2)1464 4710 y Fq(\()p Fu(S)1542 4680 y Ft(d)p Fn(\000)p Fp(1)1666 4710 y Fq(\))1698 4643 y Fl(\001)1767 4710 y Fv(is)30 b(the)g(scattering)e(matrix)h(for)g(the)h(pair)f Fr(f)p Fs(H)3112 4722 y Fp(0)3148 4710 y Fs(;)14 b(H)7 b Fr(g)p Fv(.)29 b(F)o(or)515 4810 y(shortness)19 b(we)i(shall)g(set)g Fs(')p Fq(\()p Fs(\025)p Fq(\))j(:=)f(\()p Fs(T)12 b(')p Fq(\)\()p Fs(\025;)19 b Fr(\001)5 b Fq(\))23 b Fr(2)g Fo(L)2053 4780 y Fp(2)2091 4810 y Fq(\()p Fu(S)2169 4780 y Ft(d)p Fn(\000)p Fp(1)2293 4810 y Fq(\))p Fv(.)1950 5059 y(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 704 523 a Fv(If)23 b(the)h(interaction)f Fs(V)49 b Fq(:=)29 b Fs(H)f 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Fv(is)g(a)g(symmetric)e(\002rst)i(order)f(dif)n (ferential)e(operator)h(on)h Fu(S)2892 2238 y Ft(d)p Fn(\000)p Fp(1)3047 2268 y Fv(with)h Fs(C)3292 2238 y Fp(1)3361 2268 y Fv(co-)515 2368 y(ef)n(\002cients.)26 b(Therefore)e(the)j(operator)e Fe(U)c Fs(B)1802 2380 y Fp(\006)1854 2368 y Fe(U)1942 2338 y Fn(\000)p Fp(1)2058 2368 y Fv(is)27 b(essentially)g(self)o(adjoint)f(on)g Fe(U)c Fr(D)3157 2380 y Fp(1)3194 2368 y Fv(,)27 b(and)f(its)515 2467 y(closure)19 b(is)i(decomposable)d(in)i(the)h(spectral)f (representation)e(of)i Fs(H)2484 2479 y Fp(0)2521 2467 y Fv(,)g Fj(i.e)o(.)p 1245 2617 380 4 v 1245 2688 a Fe(U)i Fs(B)1396 2700 y Fp(\006)1448 2688 y Fe(U)1535 2664 y Fn(\000)p Fp(1)1648 2688 y Fq(=)g Fe(U)p 1823 2621 115 4 v 22 w Fs(B)1886 2700 y Fp(\006)1938 2688 y Fe(U)2025 2654 y Fn(\000)p Fp(1)2138 2688 y Fr(\021)2225 2575 y Fl(Z)2308 2596 y Fn(\010)2271 2764 y Fd(R)2313 2772 y Fm(+)2378 2688 y Fq(d)p Fs(\025)14 b(B)2549 2700 y Fp(\006)2601 2688 y Fq(\()p Fs(\025)p Fq(\))p Fs(:)515 2910 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FA(Refer)n(ences)556 4621 y Fv([1])41 b(W)-8 b(.)17 b(O.)f(Amrein.)j Fj(Non-r)m(elativistic) d(quantum)e(dynamics)p Fv(,)h(v)n(olume)g(2)h(of)g Fj(Math.)f(Phys.)h (Studies)p Fv(.)695 4721 y(D.)k(Reidel)h(Publishing)e(Compan)o(y)-5 b(,)17 b(Dordrecht,)h(1981.)1950 5059 y(17)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 556 523 a Fv([2])41 b(W)-8 b(.)20 b(O.)g(Amrein)f(and)h(M.)f(B.)i(Cibils.)29 b(Global)19 b(and)h(Eisenb)n(ud-Wigner)d(time)j(delay)f(in)h(scatter)n(-)695 623 y(ing)f(theory)-5 b(.)28 b Fj(Helv)-6 b(.)20 b(Phys.)g(Acta)p Fv(,)f(60:481\226500,)e(1987.)556 789 y([3])41 b(W)-8 b(.)21 b(O.)f(Amrein,)g(M.)g(B.)h(Cibils,)g(and)f(K.)h(B.)g(Sinha.)29 b(Con\002guration)18 b(space)i(properties)f(of)h(the)695 888 y Fs(S)5 b Fv(-matrix)19 b(and)h(time)h(delay)f(in)g(potential)g (scattering.)30 b Fj(Ann.)19 b(Inst.)i(Henri)g(P)-7 b(oincar)3122 889 y(\264)3118 888 y(e)p Fv(,)19 b(47:367\226)695 988 y(382,)g(1987.)556 1154 y([4])41 b(W)-8 b(.)29 b(O.)f(Amrein)g(and)g(P) -9 b(.)28 b(Jacquet.)54 b(T)m(ime)29 b(delay)e(for)h(one-dimensional)d (quantum)i(systems)695 1254 y(with)20 b(steplik)o(e)g(potentials.)29 b(In)20 b(preparation.)556 1420 y([5])41 b(D.)32 b(Boll)5 b(\264)-33 b(e)33 b(and)e(T)-6 b(.)32 b(A.)h(Osborn.)66 b(T)m(ime)33 b(delay)e(in)h Fs(N)9 b Fv(-body)31 b(scattering.)67 b Fj(J)n(.)32 b(Math.)g(Phys.)p Fv(,)695 1519 y(20:1121\2261134,)15 b(1979.)556 1685 y([6])41 b(P)-9 b(.)22 b(A.)g(Martin.)34 b(Scattering)21 b(theory)g(with)h(dissipati)n(v)o(e)f(interactions)g (and)h(time)g(delay)-5 b(.)34 b Fj(Nuo)o(vo)695 1785 y(Cimento)20 b(B)p Fv(,)g(30:217\226238,)c(1975.)556 1951 y([7])41 b(P)-9 b(.)28 b(A.)g(Martin.)52 b(T)m(ime)28 b(delay)f(in)h(quantum)e(scattering)h(processes.)53 b Fj(Acta)28 b(Phys.)f(A)n(ustriaca)695 2051 y(Suppl.,)18 b(XXIII)p Fv(,)h(pages)h(157\226208,)d(1981.)556 2217 y([8])41 b(H.)23 b(Narnhofer)-5 b(.)36 b(Another)21 b(de\002nition)h (for)h(time)g(delay)-5 b(.)37 b Fj(Phys.)22 b(Re)o(v)-6 b(.)23 b(D)p Fv(,)g(22\(10\):2387\226239)o(0,)695 2316 y(1980.)556 2482 y([9])41 b(M.)18 b(Sassoli)i(de)f(Bianchi)f(and)g(P)-9 b(.)19 b(A.)g(Martin.)26 b(On)18 b(the)h(de\002nition)e(of)i(time)g (delay)f(in)h(scattering)695 2582 y(theory)-5 b(.)27 b Fj(Helv)-6 b(.)20 b(Phys.)g(Acta)p Fv(,)g(65\(8\):1119\2261126)o(,)15 b(1992.)515 2748 y([10])40 b(F)-7 b(.)21 b(T)-6 b(.)20 b(Smith.)29 b(Lifetime)19 b(matrix)h(in)g(collision)g(theory)-5 b(.)27 b Fj(Phys.)20 b(Re)o(v)-6 b(.)p Fv(,)20 b(118:349\226356,)15 b(1960.)515 2914 y([11])40 b(R.)28 b(T)m(iedra)f(de)h(Aldecoa.)53 b(T)m(ime)28 b(delay)g(and)f(short-range)f(scattering)h(in)h(quantum)e (w)o(a)n(v)o(e)o(g-)695 3014 y(uides.)i Fj(Ann.)20 b(Henri)g(P)-7 b(oincar)1576 3015 y(\264)1572 3014 y(e)p Fv(,)19 b(7\(1\):105\226124,) d(2006.)1950 5059 y(18)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0609150940222--