{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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 }{CSTYLE "" -1 258 "" 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 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helv etica" 1 10 0 0 255 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{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 257 25 "Moderne Physik mit Mapl e " }}{PARA 258 "" 0 "" {TEXT 258 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 5.2.4" }}{PARA 258 " " 0 "" {TEXT -1 25 "Worksheet hydrogen_10.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "c ITP Bonn \+ 1995 \+ filename: hydrogen.ms" }}{PARA 0 "" 0 "" {TEXT -1 104 "Autor: Komma \+ \+ Datum: 31.12.93" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 256 41 "Korrigierte und erg\344nzte Fassung 10.02.04" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "Index: H-Orbita le, zugeordnete Legendre-Polynome, verallgem. Laguerre-Polynome" }} {PARA 0 "" 0 "" {TEXT -1 65 "Thema: Darstellung der Wahrscheinlichkeit sdichten des H-Elektrons" }}{PARA 0 "" 0 "" {TEXT -1 84 "Synopsis: 3d- Darstellung und Polarplot der Kugelfunktionen, Plot der Radialfunktion ," }}{PARA 0 "" 0 "" {TEXT -1 94 " Wahrscheinlichkeitsd ichte als Funktion von r und theta (3d- und contour-Plot)." }}{PARA 0 "" 0 "" {TEXT -1 76 " Demonstration zur Verwendung von Prozeduren und Funktionen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "H-Orbitals" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re start:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "With(orthopoly) macht d as package bekannt, in dem die Legendre-Polynome P(l,x) zu finden sind ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "with(plots): #with(orthopoly);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "#P(5,x);#test" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "#diff(P(5,x),x$2); # test" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Man kann P( l,x) aber auch leicht selbst definieren: " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "P:=(l,x)->if l<>0 then 1/(2^l*l!)*diff((x^2-1)^l,x$ l)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " else 1 fi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "P(5,x); #test # expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 78 "Dann schreibt man eine kleine Prozedur f\374r die zugeo rdneten Legendre-Polynome:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Y:=proc(l,m,x) ; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "if m=0 the n P(l,x) else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "(1-x^2)^(m/2)*dif f(P(l,x),x$m)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Test" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "Y(5,0,u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 215 "F\374r die Plots sollte m an x durch cos(theta) ersetzen. Diese Konstruktion ist einfacher, als \+ von vornherein mit theta zu arbeiten (wegen der Ableitungen). Man ben \366tigt aber eine dummy-Variable (ebenfalls wegen diff)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "ply:=dummy->subs(dummy=cos(theta),Y (l,m,dummy));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "l:=2:m:= 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ply(poo);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Normierung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "l:='l' : m:='m': " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Ny2:=(2*l+1)*(l-m)!/(l+m)!; #Normierung^2*4*Pi" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Y(l,m,x);" }}{PARA 0 "" 0 "" {TEXT -1 61 "Kontrolle der \"spherical harmonics\" nach Vorgabe von l und m: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "l:=3:m:=2:Y(l,m,x);ply( o);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "n:='n';l:='l';m:='m';" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "Ny2*ply(o)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Nun kann man sich das Quadrat der \+ Kugelfunktion zeigen lassen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "l:=3:m:=1:\nsphereplot(Ny2*ply(o)^2,phi=Pi/2..2*Pi,theta=0..Pi, axes=boxed,scaling=constrained,grid=[15,100]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "Das i st schon ein ganz brauchbares Ma\337 f\374r die Winkelabh\344ngigkeit \+ der Aufenthaltswahrscheinlichkeit eines Elektrons." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "Nicht ganz so sch\366n, a ber informativ:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "polarplo t(Ny2*ply(o)^2,theta=0..2*Pi,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "um \+ Pi/2 gedreht zum Vergleich mit der 3d-Darstellung" }}{PARA 0 "" 0 "" {TEXT -1 54 "(und zur Demonstration eines parametrischen Aufrufes):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "polarplot([Ny2*ply(o)^2,th eta+Pi/2,theta=0..2*Pi],scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "l:='l': m:='m': n:='n':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Nun die Radialfunktion :" }}{PARA 0 "" 0 "" {TEXT -1 85 "Man ben\366tigt die verallgemeinerte n Laguerre-Polynome die im orthopoly-package stehen." }}{PARA 0 "" 0 " " {TEXT -1 39 "Wer dieses package nicht hat, schreibt:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "#u=2*r /(a*n)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "a:='a': # (Bohrsc her Radius =1, wird ggf. weiter unten benoetigt)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "l:='l': m:='m': n:='n':\nL:=(j,k,u)->if j<>0 then 1/j !*exp(u)/u^k*diff(u^(j+k)*exp(-u),u$j) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " else 1 fi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Radialfu nktion(u):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Ru:=(n,l,u)-> u^l*exp(-u/2)*L(n-l-1,2*l+1,u);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Test (l <= n-1) ... bitte genau hinschauen: l = el, 1 = eins ... oder andere Namen oder Schrifttypen w\344hlen" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "n:=3:l:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Ru(n,l,u);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Ra dialfunktion(r) und Normierung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "n:='n':l:='l':r:='r':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "plr:=u->subs(u=2*r/(n*a),simplify(Ru(n,l,u)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Nr2:=4*(n-l-1)!/(n+l)!/(a^3*n^4); #Normie rung^2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "n:=3:l:=1:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "plr(etwas);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "F\374r die Wa hrscheinlichkeitsdichte mu\337 die Radialfunktion plr = R(n,l,r) noch \+ mit r multipliziert" }}{PARA 0 "" 0 "" {TEXT -1 61 "werden, dann kann \+ man sich wieder das Quadrat zeigen lassen: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(Nr2*(r*plr(o))^2,r=0..30);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Weitere Tests" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "l:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Nr2*(r*plr(o))^2;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "n:='n';Nr2*(r*plr(o))^2;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "plot([seq(Nr2*(r*plr(o))^2, n=1..3)],r=0..30,color=[red,green,blue]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Test der Normierung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "seq(int(Nr2*(r*plr(o))^2,r=0..infinity),n=1..3);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "l:=1:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 68 "plot([seq(Nr2*(r*plr(o))^2,n=2..3)],r=0..30,co lor=[red,green,blue]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "s eq(int(Nr2*(r*plr(o))^2,r=0..infinity),n=2..3);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Will man noch die Winkelabh\344ngikeit sehen, so ste llt man das Produkt (r*R*Y)^2 am besten" }}{PARA 0 "" 0 "" {TEXT -1 80 "dreidimensional und in Polarkoordinaten dar (mit der richtigen nlm -Kombination)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "n:='n': l :='l':m:='m':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plr(o);ply (o);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Nr2*Ny2*(r*plr(etwas)*ply(o))^2;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "n:=3: l:=2:m:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Nr2*Ny2*(r*pl r(etwas)*ply(o))^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot 3d([r*cos(theta),r*sin(theta),Nr2*Ny2*(r*plr(etwas)*ply(o))^2]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " r=0..30,theta=Pi/2..2* Pi,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 248 "Nach der Ausf\374hrung des obigen Befehls kann man mit der linken Maustaste die box angeklickt halten u nd so ziehen, da\337 man das Bild von oben betrachtet. Der Plot wird \+ nach Bet\344tigen der rechten Maustaste neu aufgebaut. Man w\344hle da nn style=contour!" }}{PARA 0 "" 0 "" {TEXT -1 19 "Oder automatisiert: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "plot3d([r*cos(theta),r* sin(theta),Nr2*Ny2*(r*plr(o)*ply(o))^2]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " r=0..20,theta=0..2*Pi,axes=boxed,orienta tion=[0,0]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " shading =z,style=patchcontour,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Mit Titel \+ und ohne Achsen" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "txt:=`nl m=`||n||l||m:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "txt;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 173 "plot3d([r*cos(theta),r*sin(theta),Nr2*Ny2*(r*plr(o )*ply(o))^2], r=0..20,theta=0..2*Pi,orientation=[0,0],style=pat chcontour,scaling=constrained,shading=z,title=`txt`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 58 "Und weil das so sch\366n ist, macht m an eine procedur daraus:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "myhydrogenplots:=proc(n,l,m) global a,p1,p2,p3,p4,p5; local txt;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:= 1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#print(Y(l,m,x));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "#print(ply(o));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "txt:=`nlm=`||n||l||m:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "p1:=sphereplot(Ny2*ply(o)^2,phi=Pi/2..2*Pi,theta=0..Pi,axes=b oxed,scaling=constrained,grid=[15,100],title=`txt`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(p1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "p2:=polarplot([Ny2*ply(o)^2,theta+Pi/2,theta=0..2*Pi],scaling=constra ined,title=`txt`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(p2);" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "p3:=plot(Nr2*(r*plr(o))^2,r=0..30, title=`txt`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(p3);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "p4:=plot3d([r*cos(theta),r*sin(thet a),Nr2*Ny2*(r*plr(o)*ply(o))^2]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " r=0..30,theta=Pi/2..2*Pi,axes=boxed,title=`txt`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(p4);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "p5:=plot3d([r*cos(theta),r*sin(theta),Nr2*Ny2*(r*plr(o)*ply(o) )^2]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 " r=0..30,thet a=0..2*Pi,axes=boxed,orientation=[0,0],style=patchcontour,scaling=cons trained," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " shading=z ,title=`txt`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Bitte warten, bis alle f\374nf Plots erschienen sind." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "myhydrogenplots(4,3,0);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "In der Prozedur wurden die Plots unter Namen abgespeiche rt und k\366nnen nun weiter verwendet werden, wenn man z.B. die Option en \344ndern will." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "displ ay(p1,style=wireframe,shading=z,orientation=[56,70]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 135 "Es lohnt sich aber auch das Abspeichern der Plots in .m-files, man kann sich so eine schnell abrufbare Sammlung von \"Orbitals\" zul egen." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for n from 4 to 4 do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "for l from 0 to n-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for m from 0 to l do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "txt:=`nlm=`||n||l||m:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "#pri nt(polarplot([Ny2*ply(o)^2,theta+Pi/2,theta=0..2*Pi],scaling=constrain ed,title=`txt`));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "p||n||l||m:=pl ot3d([r*cos(theta),r*sin(theta),Nr2*Ny2*(r*plr(o)*ply(o))^2]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 " r=0..50,theta=0..2*Pi, axes=boxed,orientation=[0,0],style=contour,scaling=constrained," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " shading=z,title=`txt` ,numpoints=1000);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "print(p||n||l| |m);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "od; od; od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "Abspeichern " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "#save p4| |(0..3)||(0..3),`hydro4.m`;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#read `hydro4.m`;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#anames();" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#p411;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 49 "Das Ergebnis kann von jeder Maple-session aus mit" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "read `hyd ro4.m`;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 198 "eingelesen werden. Mit anames(); erf\344hrt man die Namen der Plo ts (allerdings auch alle anderen zugewiesenen Namen der jeweiligen ses sion -- anames(); also m\366glichst zu Beginn der session verwenden). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 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 }