{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 
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{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Definitionen der Impulsope
ratoren" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 98 "px := psi -> hbar/I*diff(psi,x);\npy := psi -> hbar/I
*diff(psi,y);\npz := psi -> hbar/I*diff(psi,z);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#pxGj+6#%$psiG6\"6$%)operatorG%&arrowGF(*(^#!\"\"\"\"
\"%%hbarGF/-%%diffG6$9$%\"xGF/F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#pyGj+6#%$psiG6\"6$%)operatorG%&arrowGF(*(^#!\"\"\"\"
\"%%hbarGF/-%%diffG6$9$%\"yGF/F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#pzGj+6#%$psiG6\"6$%)operatorG%&arrowGF(*(^#!\"\"\"\"
\"%%hbarGF/-%%diffG6$9$%\"zGF/F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 14 "Ortsoperatoren" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 59 "XX := psi -> x*psi;\nYY := psi -> y*psi;\nZZ := psi -> z*psi;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#XXGj+6#%$psiG6\"6$%)operatorG%&arr
owGF(*&%\"xG\"\"\"9$F.F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#YYGj+6#%$psiG6\"6$%)operatorG%&arrowGF(*&%\"yG\"\"\"9$F.F(F(F(6#\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ZZGj+6#%$psiG6\"6$%)operator
G%&arrowGF(*&%\"zG\"\"\"9$F.F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 20 "Drehimpulsoperatoren" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 107 "lx := psi->YY(pz(psi))-ZZ(py(psi));\nly := psi->ZZ(p
x(psi))-XX(pz(psi));\nlz := psi->XX(py(psi))-YY(px(psi));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#lxGj+6#%$psiG6\"6$%)operatorG%&arrowGF(,&-%#
YYG6#-%#pzG6#9$\"\"\"-%#ZZG6#-%#pyGF2!\"\"F(F(F(6#\"\"!" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#lyGj+6#%$psiG6\"6$%)operatorG%&arrowGF(,&-%#Z
ZG6#-%#pxG6#9$\"\"\"-%#XXG6#-%#pzGF2!\"\"F(F(F(6#\"\"!" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#lzGj+6#%$psiG6\"6$%)operatorG%&arrowGF(,&-%#XXG
6#-%#pyG6#9$\"\"\"-%#YYG6#-%#pxGF2!\"\"F(F(F(6#\"\"!" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 45 "lx(psi(x,y,z));ly(psi(x,y,z));lz(psi(x,y,
z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**^#!\"\"\"\"\"%\"yGF'%%hbar
GF'-%%diffG6$-%$psiG6%%\"xGF(%\"zGF1F'F'**F1F'F)F'-F+6$F-F(F'^#F'F'F'
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**^#!\"\"\"\"\"%\"zGF'%%hbarGF'-
%%diffG6$-%$psiG6%%\"xG%\"yGF(F0F'F'**F0F'F)F'-F+6$F-F(F'^#F'F'F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**^#!\"\"\"\"\"%\"xGF'%%hbarGF'-%%di
ffG6$-%$psiG6%F(%\"yG%\"zGF0F'F'**F0F'F)F'-F+6$F-F(F'^#F'F'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Drehimpulsquadrat" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "l2 := psi->lx(lx(psi))+ly(ly(psi))+
lz(lz(psi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l2Gj+6#%$psiG6\"6$%
)operatorG%&arrowGF(,(-%#lxG6#-F.6#9$\"\"\"-%#lyG6#-F5F1F3-%#lzG6#-F9F
1F3F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "collect
(simplify(l2(psi(x,y,z))),[x,y,z],distributed);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,4*()%%hbarG\"\"#\"\"\",&-%%diffG6$-%$psiG6%%\"xG%\"yG%
\"zG-%\"$G6$F2F'F(-F+6$F--F46$F1F'F(F()F0F'F(!\"\"*,F'F(F0F(F%F(F1F(-F
+6%F-F0F1F(F(*,F'F(F2F(F%F(F0F(-F+6%F-F0F2F(F(**F'F(F0F(F%F(-F+6$F-F0F
(F(*(F%F(,&F*F(-F+6$F--F46$F0F'F(F()F1F'F(F;*,F'F(F1F(F%F(F2F(-F+6%F-F
1F2F(F(**F'F(F1F(F%F(-F+6$F-F1F(F(*(F%F(,&F6F(FGF(F()F2F'F(F;**F'F(F2F
(F%F(-F+6$F-F2F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Kommutatore
n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Kom := (a,b,psi)->a(b(
psi))-b(a(psi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$KomGj+6%%\"aG%
\"bG%$psiG6\"6$%)operatorG%&arrowGF*,&-9$6#-9%6#9&\"\"\"-F36#-F0F4!\"
\"F*F*F*6%\"\"!F<F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "simp
lify(Kom(lx,ly,psi(x,y,z)));simplify(Kom(ly,lz,psi(x,y,z)));simplify(K
om(lz,lx,psi(x,y,z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%%hbarG\"
\"#\"\"\",&*&%\"yGF'-%%diffG6$-%$psiG6%%\"xGF*%\"zGF1F'!\"\"*&F1F'-F,6
$F.F*F'F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%%hbarG\"\"#\"\"\",&
*&%\"zGF'-%%diffG6$-%$psiG6%%\"xG%\"yGF*F2F'!\"\"*&F2F'-F,6$F.F*F'F'F'
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%%hbarG\"\"#\"\"\",&*&%\"xGF(
-%%diffG6$-%$psiG6%F+%\"yG%\"zGF3F(F(*&F3F(-F-6$F/F+F(!\"\"F(F7" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "simplify(Kom(l2,lx,psi(x,y,z
)));simplify(Kom(l2,ly,psi(x,y,z)));simplify(Kom(l2,lz,psi(x,y,z)));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 18 "Zentralsymmetrisch" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "RR := psi-> (x^2+y^2+z^2)^(n/2)*psi;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#RRGj+6#%$psiG6\"6$%)operatorG%&arrowGF(*&),(*
$)%\"xG\"\"#\"\"\"F3*$)%\"yGF2F3F3*$)%\"zGF2F3F3,$*&F2!\"\"%\"nGF3F3F3
9$F3F(F(F(6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "simpl
ify(Kom(RR,lx,psi(x,y,z)));\nsimplify(Kom(RR,ly,psi(x,y,z)));\nsimplif
y(Kom(RR,lz,psi(x,y,z)));\nsimplify(Kom(RR,l2,psi(x,y,z)));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }