{VERSION 6 0 "IBM INTEL NT" "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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }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 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 255 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 25 "Moderne Physik mit Mapl e " }}{PARA 258 "" 0 "" {TEXT 257 9 "PDF-Buch " }{URLLINK 17 "Moderne \+ Physik mit Maple" 4 "http://mikomma.de/fh/modphys.pdf" "" }}{PARA 258 "" 0 "" {TEXT -1 19 "Update auf Maple 10" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 13 "Kapitel 5.3.2" }}{PARA 258 " " 0 "" {TEXT -1 23 "Worksheet schroe_10.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 107 "c ITP Bonn 1995 \+ filename: schroe.ms" }}{PARA 0 "" 0 " " {TEXT -1 103 "Autor: Komma \+ Datum: 27.1.94" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 163 "Die Schr\366dingergleichung ist die Bewegungsglei chung der nicht relativistischen Quantenphysik. Gibt es Analogien zu d en Bewegungsgleichungen der klassischen Physik?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Schr\366dingergleichung f\374r den potentialfreien Fall (V = 0):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "sgl:=I*h*diff(psi(x,t),t)=-h^2/(2*m )*diff(psi(x,t),x$2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sglG/*(%\" hG\"\"\"-%%diffG6$-%$psiG6$%\"xG%\"tGF0F(^#F(F(,$*&#F(\"\"#F(*(F'F5%\" mG!\"\"-F*6$F,-%\"$G6$F/F5F(F(F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 196 "Eine m\366gl ichst allgemein formulierte L\366sung der SGL besteht aus einer reellw ertigen Amplitude (Funktion von Ort und Zeit) und der Wirkungsfunktion des Systems als Phase (Notation: h statt h-quer):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "u:=A(x,t)*exp(I/h*S(x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG*&-%\"AG6$%\"xG%\"tG\"\"\"-%$expG6#*(%\"hG! \"\"-%\"SGF(F+^#F+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Was pas siert, wenn wir diese Wellenfunktion in die SGL einsetzen?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "psi:=(x,t)->u;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$psiGf*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)%\"uGF)F )F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "sgl;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*(%\"hG\"\"\" ,&*&-%%diffG6$-%\"AG6$%\"xG%\"tGF0F&-%$expG6#*(F%!\"\"-%\"SGF.F&^#F&F& F&F&*,F,F&F%F5-F*6$F6F0F&F1F&F8F&F&F&F8F&,$*&#F&\"\"#F&*(F%F?%\"mGF5,* *&-F*6$F,-%\"$G6$F/F?F&F1F&F&*,^#F?F&-F*6$F,F/F&F%F5-F*6$F6F/F&F1F&F&* ,F,F&F%F5-F*6$F6FFF&F1F&F8F&F&**F,F&F%!\"#FMF?F1F&F5F&F&F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Umformen" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "gl:=sgl/u ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#glG/*,-%\"AG6$%\"xG%\"tG!\"\"- %$expG6#*(%\"hGF,-%\"SGF)\"\"\"^#F4F4F,F1F4,&*&-%%diffG6$F'F+F4F-F4F4* ,F'F4F1F,-F96$F2F+F4F-F4F5F4F4F4F5F4,$*&#F4\"\"#F4*,F'F,F-F,F1FA%\"mGF ,,**&-F96$F'-%\"$G6$F*FAF4F-F4F4*,^#FAF4-F96$F'F*F4F1F,-F96$F2F*F4F-F4 F4*,F'F4F1F,-F96$F2FHF4F-F4F5F4F4**F'F4F1!\"#FOFAF-F4F,F4F4F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gl:=simplify(gl);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#glG/*(,&*&-%%diffG6$-%\"AG6$%\"xG%\"tGF0 \"\"\"%\"hGF1F1*(F,F1-F*6$-%\"SGF.F0F1^#F1F1F1F1F,!\"\"F8F1,$*&#F1\"\" #F1*(,**&-F*6$F,-%\"$G6$F/F=F1)F2F=F1F1**^#F=F1-F*6$F,F/F1-F*6$F6F/F1F 2F1F1**F,F1-F*6$F6FCF1F2F1F8F1F1*&F,F1)FKF=F1F9F1F,F9%\"mGF9F1F9" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gl:=expand(gl);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#glG/,&**-%\"AG6$%\"xG%\"tG!\"\"-%%diffG6$F(F ,\"\"\"%\"hGF1^#F1F1F1-F/6$-%\"SGF*F,F-,**&#F1\"\"#F1**F(F-%\"mGF--F/6 $F(-%\"$G6$F+F;F1F2F;F1F-*.^#F-F1F(F-F=F--F/6$F(F+F1-F/6$F6F+F1F2F1F1* *^##F-F;F1F=F--F/6$F6F@F1F2F1F1*&#F1F;F1*&F=F-FGF;F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "Wenn diese Gleichung erf\374ll t sein soll, so mu\337 sie f\374r den Realteil und den Imagin\344rteil erf\374llt sein" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "Realteil:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "-evalc(Re(lhs(gl)))=-evalc(Re(rhs(g l)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%diffG6$-%\"SG6$%\"xG%\"tG F+,&*&#\"\"\"\"\"#F/**-%\"AGF)!\"\"%\"mGF4-F%6$F2-%\"$G6$F*F0F/%\"hGF0 F/F/*&#F/F0F/*&F5F4-F%6$F'F*F0F/F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 248 "Der Gradient der Wirkungsfuktion ist der Impuls. \+ Also steht hier die Hamilton-Jacobi-Gleichung, allerdings mit einem Zu satz, der die Dimension eines Potentials hat und mit h^2 geht. Bohm ne nnt ihn das Quantenpotential (das f\374r h -> 0 verschwindet)." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Imagin\344rteil:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "igl:=evalc(Im(lhs(gl)))=evalc(Im(rhs(gl)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$iglG/*(-%\"AG6$%\"xG%\"tG!\"\"-%%diffG6$F'F+\"\"\"% \"hGF0,&*,F'F,%\"mGF,-F.6$F'F*F0-F.6$-%\"SGF)F*F0F1F0F,*&#F0\"\"#F0*(F 4F,-F.6$F9-%\"$G6$F*F=F0F1F0F0F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "igl:=igl*A(x,t)/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$iglG/-%%diffG6$-%\"AG6$%\"xG%\"tGF-*(F)\"\"\"%\"hG!\"\",&*,F)F1%\" mGF1-F'6$F)F,F/-F'6$-%\"SGF+F,F/F0F/F1*&#F/\"\"#F/*(F4F1-F'6$F9-%\"$G6 $F,F=F/F0F/F/F1F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "igl:=e xpand(igl);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$iglG/-%%diffG6$-%\"A G6$%\"xG%\"tGF-,&*(%\"mG!\"\"-F'6$F)F,\"\"\"-F'6$-%\"SGF+F,F4F1*&#F4\" \"#F4*(F)F4F0F1-F'6$F7-%\"$G6$F,F;F4F4F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 129 "Das sieht na ch einer Kontinuit\344tsgleichung aus, wenn man n\344mlich die Amplitu de mit der Wurzel einer Teilchendichte identifiziert:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "subs(A(x,t)=sqrt(rho(x,t)),igl);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%diffG6$*$-%$rhoG6$%\"xG%\"tG#\"\" \"\"\"#F,,&*(%\"mG!\"\"-F%6$F'F+F.-F%6$-%\"SGF*F+F.F3*&#F.F/F.*(F(F-F2 F3-F%6$F8-%\"$G6$F+F/F.F.F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,$*&#\"\"\"\"\"#F'*&-% $rhoG6$%\"xG%\"tG#!\"\"F(-%%diffG6$F*F.F'F'F',&*&#F'F(F'**%\"mGF0F*F/- F26$F*F-F'-F26$-%\"SGF,F-F'F'F0*&#F'F(F'*(F*F&F8F0-F26$F=-%\"$G6$F-F(F 'F'F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "%*2*sqrt(rho(x,t)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%diffG6$-%$rhoG6$%\"xG%\"tGF+, $*(\"\"#\"\"\"F'#F/F.,&*&#F/F.F/**%\"mG!\"\"F'#F6F.-F%6$F'F*F/-F%6$-% \"SGF)F*F/F/F6*&#F/F.F/*(F'F0F5F6-F%6$F<-%\"$G6$F*F.F/F/F6F/F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%diffG6$-%$rhoG6$%\"xG%\"tGF+,&*(%\"mG!\"\"-F%6$F 'F*\"\"\"-F%6$-%\"SGF)F*F2F/*(F'F2F.F/-F%6$F5-%\"$G6$F*\"\"#F2F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 "Und dieser Zusammenhang f\374hrt bekanntlich auf die stat istische Interpretation der Quantenmechanik. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 25 "komma@oe.uni-tuebingen.de" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }