{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 18 255 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 "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" 18 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 18 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 18 0 0 0 0 0 1 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim
es" 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 "Maple Output" 0 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 0 0 0 0 0 0 -1 0 }{PSTYLE "Normal" -1 256 
1 {CSTYLE "" -1 -1 "Times" 1 18 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" -1 257 1 {CSTYLE "" -1 -1 "Times
" 1 18 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 "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 
2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 259 1 
{CSTYLE "" -1 -1 "" 1 18 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 "" 258 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 260 "" 0 "" {TEXT -1 44 "HYDROGEN WAVE FUNCTION PROBABIL
ITY DENSITIES" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 257 49 "by Corinne Manogue, Kerry Browne and Steve Sahyun" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 30 "Copyright 2004 Corinne Ma
nogue" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 206 "restart:with(plots):with(orthopoly):\nnu
mpts:=4096:\nsetoptions3d(axes=BOXED, style=patchnogrid,  numpoints=10
0000000, scaling=constrained):\nassume(r>0,theta>0,theta<Pi,phi>0,phi<
2*Pi, x,real,y,real,z,real);\n" }}}{PARA 256 "" 0 "" {TEXT -1 42 "Defi
ne the radial part of the wavefunction" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 259 "R:=proc(n,l)\nlocal B, Laguerre, Lr:\nB:=1:\nLaguerr
e[(n+l),(2*l+1)]:=\nsimplify(diff(n!*L(n+l,x),x$(2*l+1))):\nLr[(n+l),(
2*l+1)]:=subs(x=2*B*r/n,\nLaguerre[(n+l),(2*l+1)]):\n-sqrt((2*B/n)^3*(
n-l-1)!/(2*n*((n+l)!)^3))\n*(2*B*r/n)^l*exp(-B*r/n)*Lr[(n+l),(2*l+1)]
\nend:\n" }}}{PARA 257 "" 0 "" {TEXT 259 69 "Define the angular part o
f the wavefunction (the spherical harmonics)" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 230 "Y:= proc(l,m)\nlocal p, Ptheta, nrm:\np:=(1-x^2)^
(abs(m)/2)*diff(P(l,x),[x$abs(m)]):\nPtheta:=subs(x=cos(theta),p):\nnr
m:=(-1)^((m+abs(m))/2)*sqrt((2*l+1)*factorial(l-abs\n(m))/(4*Pi*factor
ial(l+abs(m)))):\nnrm*Ptheta*exp(I*m*phi)\nend:\n" }}}{PARA 0 "" 0 "" 
{TEXT -1 1 "\n" }{TEXT 266 57 "Choose the quantum numbers for the quan
tum state |n,el,m>" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "n:=2:e
l:=1:m:=1:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 25 "Plot the a
ngular part of " }{XPPEDIT 257 0 "abs(Phi[n,el,m](r,theta,phi))^2;" "6
#*$-%$absG6#-&%$PhiG6%%\"nG%#elG%\"mG6%%\"rG%&thetaG%$phiG\"\"#" }
{TEXT 264 2 "  " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ylmsq:=(a
bs(Y(el,m)))^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ylmsqG,$*&#\"\"$
\"\")\"\"\"*&%#PiG!\"\",&F*F**$)-%$cosG6#%'theta|irG\"\"#F*F-F*F*F*" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "sphereplot(1, phi=0..2*Pi,
 theta=0..Pi, \ncolor=ylmsq, numpoints=numpts);" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 267 24 "Plot the radial part of \+
" }{XPPEDIT 258 0 "abs(Phi[n,l,m](r,theta,phi))^2;" "6#*$-%$absG6#-&%$
PhiG6%%\"nG%\"lG%\"mG6%%\"rG%&thetaG%$phiG\"\"#" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 97 "maxr:=2*n^2:\nif (el=0) then minr:=1 else minr
:=0 fi:\nplot(conjugate(R(n,el))*R(n,el),r=0..maxr);\n" }}}{PARA 257 "
" 0 "" {TEXT -1 1 "\n" }{TEXT 268 65 "Schroedinger's wavefunction and \+
its square for the hydrogen atom." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "Psiex:= R(n,el)*Y(el,m);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&PsiexG,$*&#\"\"\"\"#CF(*,%#r|irGF(-%$expG6#,$*&\"\"#
!\"\"F+F(F2F(%#PiG#F2F1,&F(F(*$)-%$cosG6#%'theta|irGF1F(F2#F(F1-F-6#*&
%%phi|irGF(^#F(F(F(F(F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "
Psiexsq:=(abs(Psiex))^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(Psiexsq
G,$*&#\"\"\"\"$w&F(**%#r|irG\"\"#-%$expG6#,$*&F,!\"\"F+F(F2F,%#PiGF2,&
F(F(*$)-%$cosG6#%'theta|irGF,F(F2F(F(F(" }}}{EXCHG {PARA 259 "" 0 "" 
{TEXT -1 51 "Calculate a scaling factor for the upcoming graphs:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "fmin:=0: \nfmax:=(maximize(
Psiexsq,r=minr..maxr, theta=0..3.15, phi=0..6.3));\nscale:=evalf[1](1/
fmax);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fmaxG$\"+qlc\"*H!#8" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&scaleG$\"\"$F&" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 103 "CPsiexsqxyz:=scale*subs(r=sqrt(x^2+y^2+z^2)
, theta=arctan(sqrt(x^2+y^2)/z), phi=arctan(y/x), Psiexsq);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,CPsiexsqxyzG,$*,$\"+LLL3_!\"*\"\"\"
,(*$)%#x|irG\"\"#F*F**$)%#y|irGF/F*F**$)%#z|irGF/F*F*F*-%$expG6#,$*&F/
!\"\"F+#F*F/F;F/%#PiGF;,&F*F**$)-%$cosG6#-%'arctanG6#*&,&F,F*F0F*F<F5F
;F/F*F;F*F*" }}}{PARA 257 "" 0 "" {TEXT 260 35 "Plots of the spatial d
ependence of " }{XPPEDIT 261 0 "abs(Phi[n,l,m](r,theta,phi))^2;" "6#*$
-%$absG6#-&%$PhiG6%%\"nG%\"lG%\"mG6%%\"rG%&thetaG%$phiG\"\"#" }{TEXT 
262 2 " \n" }{TEXT -1 43 "Animation of y-z plane probability surfaces
" }}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 201 "Psixsectionplot:=seq(
plot3d([xval,y,z],y=-maxr..maxr, z=-maxr..maxr,\ncolor=subs(x=xval,CPs
iexsqxyz),numpoints=numpts,\nview=[-maxr..maxr,-maxr..maxr, -maxr..max
r]), xval=seq((j*maxr/15)+.1, j=-15..15)):" }}{PARA 257 "> " 0 "" 
{MPLTEXT 1 0 63 "display(Psixsectionplot, insequence=true, scaling=con
strained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 43 "Ani
mation of x-y plane probability surfaces" }}}{EXCHG {PARA 257 "> " 0 "
" {MPLTEXT 1 0 203 "Psizsectionplot:=seq(plot3d([x,y,zval],\nx=-maxr..
maxr, y=-maxr..maxr,\ncolor=subs(z=zval,CPsiexsqxyz),numpoints=numpts,
\nview=[-maxr..maxr,-maxr..maxr, -maxr..maxr]), \nzval=seq((j*maxr/15)
+.1, j=-15..15)):" }}{PARA 257 "> " 0 "" {MPLTEXT 1 0 63 "display(Psiz
sectionplot, insequence=true, scaling=constrained);" }}}{PARA 257 "" 
0 "" {TEXT -1 44 "\nAnimation of x-z plane probability surfaces" }}
{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 203 "Psiysectionplot:=seq(plot
3d([x,yval,z],\nx=-maxr..maxr, z=-maxr..maxr, \ncolor=subs(y=yval,CPsi
exsqxyz),numpoints=numpts,\nview=[-maxr..maxr,-maxr..maxr, -maxr..maxr
]), yval=seq((j*maxr/15)+.1, j=-15..15)):" }}{PARA 257 "> " 0 "" 
{MPLTEXT 1 0 63 "display(Psiysectionplot, insequence=true, scaling=con
strained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2
9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
}