{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "int(sin(x)^2, x=0..n *Pi)/(n*Pi) assuming n::integer;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6## \"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "psi := n -> \+ sqrt(2/L)*sin(n*Pi*x/L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$psiGf*6 #%\"nG6\"6$%)operatorG%&arrowGF(*&-%%sqrtG6#,$*&\"\"#\"\"\"%\"LG!\"\"F 3F3-%$sinG6#**9$F3%#PiGF3%\"xGF3F4F5F3F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(psi(n)*psi(m), x=0..L) assuming n::integer, \+ m::integer;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(psi(n)^2, x=x0..x0+dx) assuming n::in teger, m::integer;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,(*(-%$cosG6#* *%\"nG\"\"\"%#PiGF+%#x0GF+%\"LG!\"\"F+-%$sinGF(F+F.F+F+*(-F'6#**F*F+F, F+,&F-F+%#dxGF+F+F.F/F+-F1F4F+F.F+F/*(F*F+F,F+F7F+F+F+F*F/F,F/F.F/" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(%, n=infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#dxG\"\"\"%\"LG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "psi1 := n -> eval(psi(n), L=1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%psi1Gf*6#%\"nG6\"6$%)operatorG%&arr owGF(-%%evalG6$-%$psiG6#9$/%\"LG\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "psi1(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\" \"##\"\"\"F$-%$sinG6#,$*(F$F&%#PiGF&%\"xGF&F&F&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "plot(psi1(100), x=0.9..1);" }}{PARA 13 "" 1 " " {GLPLOT2D 471 471 471 {PLOTDATA 2 "6%-%'CURVESG6$7iw7$$\"3A+++++++!* !#=$!3]4FmwshQb!#K7$$\"3/n;a)G\\a+*F*$\"3AwcpklC4CF*7$$\"3vKL3x&)*3,*F *$\"3nW&*4@j0[ZF*7$$\"3d**\\ilyM;!*F*$\"3Q.7,S88FG7$$\"3$om\"zp!fu1*F*$\"3l(Hh4Wkn?\"FG7$$\"3r mmm6m#G2*F*$\"3h3!4:'e*e1\"FG7$$\"3fm;a`T>y!*F*$\"3ml)e@l/z%*)F*7$$\"3 ZmmT&phN3*F*$\"3EE.>+2$[F*7$$\"3; +v=ddC%4*F*$\"3VmB;55kUDF*7$$\"3-7$$\"3 'QLe*=)H\\5*F*$!3>T[UQ`^\"=#F*7$$\"33nmTlD))4\"*F*$!3T%=v@U40K%F*7$$\" 3H+](=JN[6*F*$!3OhiC;b6bjF*7$$\"3]LLLe!)y>\"*F*$!3nXHtEa?\"H7FG7$$\"3B++]2`vr\"*F*$!3+?q_0xc'4\"FG7$$\"3 ?L$3_(>/x\"*F*$!35mH\")p]OQ$*F*7$$\"3*F*$!3;`HU?v*=1$F*7$$\"3u m\"HdG\"\\)>*F*$!31o\">=SJ0q'Fbr7$$\"3a]7Gt#HR?*F*$\"35%F*7$$\"3^n\"HK/dT@*F*$\"3g0,Ckp[%3'F*7$$ \"3n+]iDo%*=#*F*$\"3$Ge&G0(3&HzF*7$$\"3%Q$3-3mtB#*F*$\"3udW:5AK&f*F*7$ $\"3+nmT!RE&G#*F*$\"3!)[`A\")zU/6FG7$$\"3$GLe9r5$R#*F*$\"3Dhoo,!>_L\"F G7$$\"3w****\\K]4]#*F*$\"3q]Ekfs?99FG7$$\"3:+++NO#4E*F*$\"3N$p0jy^*ppF*F*$\"3pCZ*)RD Qi$*F*7$$\"3_++]-w=#G*F*$\"3h#*[j8'Hs](F*7$$\"32,++&G0uG*F*$\"31^%pOa9 3X&F*7$$\"3]++]nHi#H*F*$\"3Cqff()zE[KF*7$$\"3'p\"H2B6O(H*F*$\"3D$fe^gz 5<\"F*7$$\"3TLeky#*4-$*F*$!3)QrK1b*3?$*Fbr7$$\"3()\\(=UVPoI*F*$!3YmclU Z[9IF*7$$\"3Lm;z*ev:J*F*$!3KqZ^*o!HI]F*7$$\"3%Q3_]r4sJ*F*$!32?0bYY(*ys F*7$$\"3C+DJSQ%GK*F*$!3'G\"eU0r?+$*F*7$$\"3k;HdlzZG$*F*$!3&HLIA\"H3.6F G7$$\"3/LL$347TL*F*$!3T-;DninT7FG7$$\"3_L$eR$\\))Q$*F*$!3!fmc6%f')G8FG 7$$\"3+ML3xxlV$*F*$!3'**Gy.nMiQ\"FG7$$\"3CMek)>WgM*F*$!3tMa\\HoI.9FG7$ $\"3\\M$3-iI%[$*F*$!3UA58\\]\\79FG7$$\"3iL3xTq\"3N*F*$!3nF$3)3xu89FG7$ $\"3'QLLLY.KN*F*$!3*z#4%4xdqS\"FG7$$\"3:]7`9ave$*F*$!3i_Z\"3$>0h8FG7$$ \"3bn\"HdO2VO*F*$!3?=j\"QsWPF\"FG7$$\"3&Q3FpJf)p$*F*$!3B*>CH]&yZ6FG7$$ \"39+]7o7Tv$*F*$!3$*)3aYBl*p)*F*7$$\"3O$3xcoD.Q*F*$!3;l72zA/&>)F*7$$\" 3em\"HK5S_Q*F*$!3k%Q.!*Hl^K'F*7$$\"3!)\\7y?X:!R*F*$!3sB^i\"H<[I%F*7$$ \"3+LLLQ*o]R*F*$!3-D-6\\31#=#F*7$$\"3/]7GL3Y+%*F*$\"3NO;\\+oNZ?Fbr7$$ \"32n\"H#GF&eS*F*$\"3Y7d,s;n&e#F*7$$\"35%3xJiW7T*F*$\"3G.#)y&3$f#*[F*7 $$\"3-+]7=lj;%*F*$\"3F1m$)RXYfqF*7$$\"3%3](=x3x@%*F*$\"3GmFtT!oe$*)F*7 $$\"3a++DO_!pU*F*$\"3l#e;xEG!e5FG7$$\"3D+DJ&fR?V*F*$\"3%yX;:p,]>\"FG7$ $\"3&***\\PaR6`U%*F*$\"33G*RL$3Y v8FG7$$\"3tm\"zWG))yW*F*$\"3VDE4*e-6T\"FG7$$\"3(y?0q'oc]%*F*$\"3_IGt5$ *)RT\"FG7$$\"37]7`\\aC`%*F*$\"3*=)o^I\"poS\"FG7$$\"3P#Hd?.CfX*F*$\"3:3 7YQCz*Q\"FG7$$\"3^LLe9Ege%*F*$\"3z#Fbr7$$\"3p;/wn#=]] *F*$!3@%\\n[GL.A#F*7$$\"3HmT5D,`5&*F*$!3sqpuIYa$f%F*7$$\"3)e\"zW#)>/;& *F*$!3Y.)[)4]OHoF*7$$\"3em;zRQb@&*F*$!3#Qa#G&)>#4'))F*7$$\"3t*\\7y#>NE &*F*$!3ZH0O%\\d:/\"FG7$$\"3*RLLe,]6`*F*$!3\"fa;H'=St6FG7$$\"38nT&Q5[f` *F*$!3S1L.w_jy7FG7$$\"3G+](=>Y2a*F*$!3fBHA,7([N\"FG7$$\"3V3-8DsLV&*F*$ !3oU9@UbM$Q\"FG7$$\"3f;aQe#Gfa*F*$!3ZWq7;!fES\"FG7$$\"3uC1k\"H>&[&*F*$ !3-z&=Us$o79FG7$$\"3*G$e*[K56b*F*$!3md9C(F*7$$\"3h+DJ?i7)e *F*$!3dR/.fj)Q:&F*7$$\"3;+]ibOO$f*F*$!3,C*z*\\l8FHF*7$$\"3o*\\P44,')f* F*$!3]7ut*p)=8iFbr7$$\"3M++DE&QQg*F*$\"3eW%ex)=G,'*F *$\"3vWv1+^6kzF*7$$\"3q**\\7y%3Ti*F*$\"3$Ra5$zZ.;(*F*7$$\"3J]7`f]tH'*F *$\"3AKG>PW;P6FG7$$\"3\")*\\P4kh`j*F*$\"3xHCICkGn7FG7$$\"3I\\PMA#))4k* F*$\"3kVO@uU\"zN\"FG7$$\"3\"****\\P![hY'*F*$\"386mNIOA19FG7$$\"3k;HdqE 9\\'*F*$\"3g/'psj+PT\"FG7$$\"3OLeRP0n^'*F*$\"3Ma'*F*$\"3`+=KA+$>S\"FG7$$\"3\"omT5FEnl*F*$\"3!=v3ifcFQ\"FG7$$\"3E+vo/ ?yh'*F*$\"3,jTpSqV=8FG7$$\"3rLLLQx$om*F*$\"3DZc2Xp#4A\"FG7$$\"3!3+DJ\" eBs'*F*$\"3EZ'3!4A'H3\"FG7$$\"3zmm\"z)Qjx'*F*$\"37b#4Iko#R\"*F*7$$\"3x K$3F'>.$o*F*$\"3WZM&*4gq'=(F*7$$\"3()****\\P+V)o*F*$\"3uT'y_(R&z-&F*7$ $\"3M;Hd&\\@Lp*F*$\"3_zr>u&fa%HF*7$$\"3!G$ek`H@)p*F*$\"32-A\"**fna$zFb r7$$\"3Q](=iE;$oqP\"F*7$$\"3%om\"zpe*zq*F*$!3[q5sH(G_^$F* 7$$\"3Y\\(oa_VLr*F*$!3R@*eNBhiv&F*7$$\"3>Le9\"=\"p=(*F*$!3\"4af!zx?NyF *7$$\"3#p\"H#o$)QSs*F*$!3'QyBC(*GNp*F*7$$\"3l++]#\\'QH(*F*$!35'owKy*)y 7\"FG7$$\"3Am\"zp%*\\%R(*F*$!3)*R#Q^wWsL\"FG7$$\"3!HLe9S8&\\(*F*$!38(4 U8K[ST\"FG7$$\"3'omT5hK+w*F*$!3\"39lDf[XM\"FG7$$\"3s**\\i?=bq(*F*$!3v( Hki-T&H6FG7$$\"3b$3xc/%pv(*F*$!3m*QE#*R*fz(*F*7$$\"3Gm\"H2FO3y*F*$!3\" )z,Dg#=\"4!)F*7$$\"3,\\7y&\\yfy*F*$!3z;+u&*=2IgF*7$$\"3%GLL3s?6z*F*$!3 K`,&pf'*R*QF*7$$\"3=\\i!R:/lz*F*$!3!3mY,6V+b\"F*7$$\"3im\"zpe()=!)*F*$ \"3@-fOEPT\"Q)Fbr7$$\"32%3_+-rs!)*F*$\"3Te3V7#4C?$F*7$$\"3S+]7`Wl7)*F* $\"3rCUjR_HvaF*7$$\"3$oT5!R$Ry\")*F*$\"3'*p*4G)4Pk&R(ob4\"FG7$$\"3Dnmm'* RRL)*F*$\"3o\"**\\oC!4E7FG7$$\"3dnTN\"H'pQ)*F*$\"3d\\AG9^(fK\"FG7$$\"3 ym;/'e)*R%)*F*$\"3W=dOz@:*Q\"FG7$$\"38UNrfTKX)*F*$\"37C5`_F)*)R\"FG7$$ \"3Q;aQL(\\m%)*F*$\"3M!=JS^(Q19FG7$$\"3j!HdqIvz%)*F*$\"3^m!RTi`8T\"FG7 $$\"3*f;H2)3I\\)*F*$\"3*e[1&)*F*$\"3^%)Hvf^b69FG7$$\"31#zW`5%=Is 19FG7$$\"3JmmTvJga)*F*$\"3W$3^')*F*$\"3t*)3Lw] kd7FG7$$\"3wL$e9tOc()*F*$\"3s!e6yhxzz*F*7$$\"3a\\P%[ko/))*F*$\"3hzCbLd >V\")F*7$$\"3Um\"H#e0I&))*F*$\"33:3[j18,jF*7$$\"3K$e9;ZK,*)*F*$\"3VGLi qv99VF*7$$\"3?+++&Qk\\*)*F*$\"3?X1%*[X%zA#F*7$$\"3yK3-.B]+**F*$!3+;$G4 !4eJAFbr7$$\"3[m;/@-/1**F*$!39v)>)fI_nEF*7$$\"3=+D1R\"y:\"**F*$!3_:?09 #\\8.&F*7$$\"3xKL3dg6<**F*$!3-S'yM1nKC(F*7$$\"3Km\"zpBp?#**F*$!3PK[>lq @Q!*F*7$$\"3()**\\(oTAq#**F*$!3-v)Q?iv91\"FG7$$\"3TL3x'fv>$**F*$!3C6aP 0(yM>\"FG7$$\"3'pmmmxGp$**F*$!39+S(z1TmH\"FG7$$\"3B]7`**)4A%**F*$!3Ot \"HZ#G2s8FG7$$\"3\\LeRA5\\Z**F*$!31MEJjE#)49FG7$$\"3oD\"GQeJ,&**F*$!3O #zs*y9?99FG7$$\"3w;/EX@x_**F*$!3*zNQ6%Q&)39FG7$$\"3%yq#p1FTb**F*$!3;\" *zDHl\"QR\"FG7$$\"3-+]7oK0e**F*$!3M39XlH>p8FG7$$\"3p*\\il(z5j**F*$!3g: XD[$))fH\"FG7$$\"3O*****\\oi\"o**F*$!3KH%Q._r,>\"FG7$$\"3-*\\PMRnU-zC%z#pF*7$$\"3M*\\P40O\"*)**F*$!3;hkW(phNt%F*7$$\"3o\\(oa-oX ***F*$!34\\rJWim,CF*7$$\"\"\"\"\"!$\"3HlCWYB1yFF--%'COLOURG6&%$RGBG$\" *++++\"!\")$Fd[oFd[oF^\\o-%+AXESLABELSG6$%\"xGQ!6\"-%%VIEWG6$;$\"\"*! \"\"Fb[o%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "5 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }