{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Worksheet zu Aufgabe 6" }} {PARA 0 "" 0 "" {TEXT -1 24 "Gerald Schubert 04.11.03" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Hermite-Polynome" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Hermite H(1,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "HermiteH(2,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 15 "HermiteH(15,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 40 "Klassische Aufenthaltswahrscheinlichkeit" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "P_kl := x0 -> unapply(1/(Pi*x0)*1/sqrt(1-(x/x0)^2) ,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "integrate(P_kl(1)(x ),x=-1..1);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 48 "Quantenmechanisc he Aufenthaltswahrscheinlichkeit" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "P_qm := n -> unapply(1/(n!*2^n*sqrt(Pi))*(HermiteH(n,x))^2*exp (-x^2),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "P_qm(1)(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Vergleich" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "plot([P_qm(1)(x),P_qm(2)(x),P_qm(15)(x)],x=-7..7,colo r=[red,green,blue],thickness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "plot ([P_qm(1)(x),P_kl(sqrt(3))(x)],x,view=[-3..3,0.. 0.8],color=[red,black],thickness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "plot ([P_qm(2)(x),P_kl(sqrt(5))(x)],x,view=[-3.5..3.5 ,0..0.6],color=[green,black],thickness=3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 92 "plot ([P_qm(15)(x),P_kl(sqrt(31))(x)],x,view=[-7..7 ,0..0.4],color=[blue,black],thickness=3);" }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 51 "Skalierung auf die klassische Oszillationsamplitude" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Es ist klar, da\337 f\374r den kla ssischen Oszillator gilt x0=x0(E)." }}{PARA 0 "" 0 "" {TEXT -1 135 "Au ch im quantenmechanischen Fall sind die Wellenfunktionen der h\366here nergetischen Eigenenergien \374ber einen gr\366\337eren Bereich ausged ehnt." }}{PARA 0 "" 0 "" {TEXT -1 147 "Um trotzdem einen qualitativen \+ Vergleich zu erm\366glichen, bietet sich eine Skalierung auf die klass ische Oszillatoramplitude zugeh\366riger Energie an:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 263 "plot([sqrt(3)*P_qm(1)(x*sqrt(3)),\n sqrt(5 )*P_qm(2)(x*sqrt(5)),\n sqrt(31)*P_qm(15)(x*sqrt(31)),\n P_k l(1)(x)],\n x,\n view=[-2..2,0..2],\n color=[red,green, blue,black],\n linestyle=[DASH,SOLID,DOT,DASHDOT],\n thickne ss=[3,3,2,3]);" }}}}}{MARK "5 1 0 0" 47 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }