{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }{CSTYLE "_cstyle1" -1 201 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 0 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 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 1 0 1 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 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 1 0 1 0 2 2 -1 1 } {PSTYLE "_pstyle1" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 0 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle5" -1 204 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "# This sheet comput es solutions to the schrodinger equation with\n# Gaussian initial cond itions and a zero potential" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 21 "restart:\nwith(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning , the name changecoords has been redefined\n" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 201 42 "# This is the integral we want to evaluate" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 105 "sqrt(2*m/(hb*t)) * I nt( exp( -(sqrt(2*m/(hb*t))*k)^2 ) * exp(-I*k^2)*exp(I*k*eta),k=-infin ity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(-%%sqrtG6#\"\"#\" \"\"-F%6#*(%\"mGF(%#hbG!\"\"%\"tGF.F(-%$IntG6$*(-%$expG6#,$**F,F(F-F.F /F.%\"kGF'!\"#F(-F56#*&^#F.F()F9F'F(F(-F56#*(^#F(F(F9F(%$etaGF(F(/F9;, $%)infinityGF.FHF(" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 30 "h b := 1; m := 1;\n#assume(t>0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h bG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\"\"\"" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 101 "# I would like to assume t>0 h ere so that the integral is cleaner but\n# that causes problems later. .." }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 113 "blah := sqrt(2*m /(hb*t)) * int( exp( -(sqrt(2*m/(hb*t))*k)^2 ) * exp(-I*k^2)*exp(I*k*e ta),k=-infinity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%blah G*(-%%sqrtG6#\"\"#\"\"\"-F'6#*&F*F*%\"tG!\"\"F*-%*PIECEWISEG6$7$*(-%$e xpG6#,$*(F.F*%$etaGF),&F)F**&^#F*F*F.F*F*F/#F/\"\"%F**&F;F*F.F/#F/F)%# PiG#F*F)/-%%csgnG6#,&F-F)F=F*F*7$%)infinityG%*otherwiseGF*" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 71 "# main animations loop, generat es the frame and stores them in a list L" }}}{EXCHG {PARA 200 "> " 0 " " {MPLTEXT 1 201 354 "h := 1/2; # time step\nN := 10;\nfudge := 1/100 00; # prevent t from being zero\nL := [];\nfor n from 0 to N do\n t \+ := n*h + fudge:\n # substitue for eta to obtain an expression in x\n \+ blah2 := subs(eta = x/sqrt(hb*t/(2*m)), blah): \n p := plot([sqrt(R e(blah2)^2 + Im(blah2)^2), Re(blah2), Im(blah2)], x=-20..20, color=[bl ue,red,green]):\n L := [op(L), p]:" }{MPLTEXT 1 201 4 "\nod:" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG#\"\"\"\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"NG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&fudg eG#\"\"\"\"&++\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7\"" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 35 "type(L,list); # L *must * be a list" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 36 "# blue=modulus, red=real, green =imag" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 28 "display(L, ins equence=true);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 400 400 {PLOTDATA 2 " 6#-%(ANIMATEG6-7'-%'CURVESG6$7_p7$$!#?\"\"!$\"+GYm$f'!#`7$$!+$Q6G\">! \")$\"+[>PNL!#\\7$$!+M!\\p$=F5$\"+!H#p*3%!#Y7$$!+))Qj^!#E7$$!+d4`i6F5$\"+1L7fP!#C7$$!+QW*e3\"F5$\"+X]7#z#!#A7$$!*q )>'***F5$\"+.%)z3DF-7$$!*]5*H\"*F5$\"+'yN!z:!#=7$$!*I\"3&H)F5$\"+a)e^* f!#<7$$!*Twp`(F5$\"+11([?\"!#:7$$!*P;bj'F5$\"+QL7QH!#97$$!*Zh=(eF5$\"+ 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