{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 "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "assume(kappa1>0);assume(kappa2>0); assume(N100>0);assume(N200>0);assume(N210,real);assume(N211>0);assume( N21m1,real);assume(r>0);assume(theta,real);assume(phi,real);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "psi100 := N100*exp(-kappa1*r )/sqrt(4*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'psi100G,$*&#\"\"\" \"\"#F(*(%&N100|irGF(-%$expG6#,$*&%(kappa1|irGF(%#r|irGF(!\"\"F(%#PiG# F3F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "psi200 := N200* exp(-kappa2*r)*(1-kappa2*r)/sqrt(4*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'psi200G,$*&#\"\"\"\"\"#F(**%&N200|irGF(-%$expG6#,$*&%(kappa2| irGF(%#r|irGF(!\"\"F(,&F(F(F0F3F(%#PiG#F3F)F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 67 "psi210 := N210*exp(-kappa2*r)*2*kappa2*r*sqrt( 3/(4*Pi))*cos(theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'psi210G*0% &N210|irG\"\"\"-%$expG6#,$*&%(kappa2|irGF'%#r|irGF'!\"\"F'F-F'F.F'\"\" $#F'\"\"#%#PiG#F/F2-%$cosG6#%'theta|irGF'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 160 "psi211 := N211*exp(-kappa2*r)*2*kappa2*r*sqrt(3/(8 *Pi))*sin(theta)*exp(I*phi);\npsi21m1 := N21m1*exp(-kappa2*r)*2*kappa2 *r*sqrt(3/(8*Pi))*sin(theta)*exp(-I*phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'psi211G,$*&#\"\"\"\"\"#F(*2%&N211|irGF(-%$expG6#,$*& %(kappa2|irGF(%#r|irGF(!\"\"F(F1F(F2F(\"\"'F'%#PiG#F3F)-%$sinG6#%'thet a|irGF(-F-6#*&%%phi|irGF(^#F(F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(psi21m1G,$*&#\"\"\"\"\"#F(*2%'N21m1|irGF(-%$expG6#,$*&%(kappa2|i rGF(%#r|irGF(!\"\"F(F1F(F2F(\"\"'F'%#PiG#F3F)-%$sinG6#%'theta|irGF(-F- 6#*&^#F3F(%%phi|irGF(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "conjugate(psi211);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\" \"\"#F&*2%&N211|irGF&-%$expG6#,$*&%(kappa2|irGF&%#r|irGF&!\"\"F&F/F&F0 F&\"\"'F%%#PiG#F1F'-%$sinG6#%'theta|irGF&-F+6#*&%%phi|irGF&^#F&F&F1F&F &" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "i100100 := int(int(int (psi100*psi100*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(i100100G,$*(\"\"%!\"\"%&N100|i rG\"\"#%(kappa1|irG!\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "nn100 := solve(i100100=1,N100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&nn100G6$,$*&\"\"#\"\"\")%(kappa1|irG#\"\"$F(F)F),$*&F(F)F*F)!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "psi100n := subs(N100 =nn100[1],psi100);\nint(int(int(conjugate(psi100n)*psi100n*r^2*sin(the ta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(psi100nG*(%(kappa1|irG#\"\"$\"\"#-%$expG6#,$*&F&\"\" \"%#r|irGF/!\"\"F/%#PiG#F1F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "i200200 := int(int(int (conjugate(psi200)*psi200*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),t heta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(i200200G,$*(\"\"%! \"\"%&N200|irG\"\"#%(kappa2|irG!\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "nn200 := solve(i200200=1,N200);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&nn200G6$,$*&\"\"#\"\"\")%(kappa2|irG#\"\"$F(F)F),$ *&F(F)F*F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "psi200n := subs(N200=nn200[1],psi200);\nint(int(int(conjugate(psi200n)*psi200 n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(psi200nG**%(kappa2|irG#\"\"$\"\"#-%$expG6 #,$*&F&\"\"\"%#r|irGF/!\"\"F/,&F/F/F.F1F/%#PiG#F1F)" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "i210210 := int(int(int(conjugate(psi210)*psi210*r^2*sin(theta),r=0..i nfinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%(i210210G,$*(\"\"$\"\"\"%&N210|irG\"\"#%(kappa2|irG!\"$F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "nn210 :=solve(i210210=1,N210 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&nn210G6$,$*(\"\"$!\"\"F(#\"\" \"\"\"#%(kappa2|irG#F(F,F+,$*(F(F)F(F*F-F.F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "psi210n := subs(N210=nn210[1],psi210);\nint(int (int(conjugate(psi210n)*psi210n*r^2*sin(theta),r=0..infinity),phi=0..2 *Pi),theta=0..Pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%(psi210nG*,%(kappa2|irG#\"\"&\"\"#-%$expG6#,$* &F&\"\"\"%#r|irGF/!\"\"F/F0F/%#PiG#F1F)-%$cosG6#%'theta|irGF/" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 213 "i211211 := int(int(int(conjugate(psi211)*psi211*r^2* sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);\ni21m121m1 := int (int(int(conjugate(psi21m1)*psi21m1*r^2*sin(theta),r=0..infinity),phi= 0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(i211211G, $*(\"\"$\"\"\"%&N211|irG\"\"#%(kappa2|irG!\"$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*i21m121m1G,$*(\"\"$\"\"\"%'N21m1|irG\"\"#%(kappa2|ir G!\"$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "nn211 := solve(i 211211=1,N211);nn21m1 := solve(i21m121m1=1,N21m1);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&nn211G6$,$*(\"\"$!\"\"F(#\"\"\"\"\"#%(kappa2|irG#F (F,F+,$*(F(F)F(F*F-F.F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'nn21m1G6 $,$*(\"\"$!\"\"F(#\"\"\"\"\"#%(kappa2|irG#F(F,F+,$*(F(F)F(F*F-F.F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "psi211n := subs(N211=nn211 [1],psi211);\nint(int(int(conjugate(psi211n)*psi211n*r^2*sin(theta),r= 0..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "psi21m1n := subs(N21m1=nn21m1[1],psi21m1);\nint(int(int(conju gate(psi21m1n)*psi21m1n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),the ta=0..Pi);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(psi211nG,$*&#\"\"\"\"\"'F(*2\"\"$#F(\"\"#%(kappa2|ir G#\"\"&F--%$expG6#,$*&F.F(%#r|irGF(!\"\"F(F6F(F)F,%#PiG#F7F--%$sinG6#% 'theta|irGF(-F26#*&%%phi|irGF(^#F(F(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)psi21m1nG, $*&#\"\"\"\"\"'F(*2\"\"$#F(\"\"#%(kappa2|irG#\"\"&F--%$expG6#,$*&F.F(% #r|irGF(!\"\"F(F6F(F)F,%#PiG#F7F--%$sinG6#%'theta|irGF(-F26#*&^#F7F(%% phi|irGF(F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "int(int(int(conjugate(psi100n)*e*r *cos(theta)*psi100n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0 ..Pi);\nint(int(int(conjugate(psi100n)*e*r*sin(theta)*cos(phi)*psi100n *r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);\nint(int(int (conjugate(psi100n)*e*r*sin(theta)*sin(phi)*psi100n*r^2*sin(theta),r=0 ..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "int(int(int(conjugate(psi100n)*e*r*cos(theta)*psi200n*r^2*sin(theta), r=0..infinity),phi=0..2*Pi),theta=0..Pi);\nint(int(int(conjugate(psi10 0n)*e*r*sin(theta)*cos(phi)*psi200n*r^2*sin(theta),r=0..infinity),phi= 0..2*Pi),theta=0..Pi);\nint(int(int(conjugate(psi100n)*e*r*sin(theta)* sin(phi)*psi200n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..P i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "int(int(int(conjugate(psi10 0n)*e*r*cos(theta)*psi210n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi), theta=0..Pi);\nint(int(int(conjugate(psi100n)*e*r*sin(theta)*cos(phi)* psi210n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);\nint( int(int(conjugate(psi100n)*e*r*sin(theta)*sin(phi)*psi210n*r^2*sin(the ta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"#K\"\"\"%(kappa1|irG#\"\"$\"\"#%\"eGF&%(kappa2|ir G#\"\"&F*,.*$)F'F.F&F&*(F.F&)F'\"\"%F&F,F&F&*(\"#5F&)F'F)F&)F,F*F&F&*( F6F&)F'F*F&)F,F)F&F&*(F.F&F'F&)F,F4F&F&*$)F,F.F&F&!\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "int(int(int(conjugate( psi100n)*e*r*cos(theta)*psi211n*r^2*sin(theta),r=0..infinity),phi=0..2 *Pi),theta=0..Pi);\nint(int(int(conjugate(psi100n)*e*r*sin(theta)*cos( phi)*psi211n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi); \nint(int(int(conjugate(psi100n)*e*r*sin(theta)*sin(phi)*psi211n*r^2*s in(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"#;\"\" \"%(kappa1|irG#\"\"$\"\"#%\"eGF&%(kappa2|irG#\"\"&F*F*#F&F*,.*$)F'F.F& F&*(F.F&)F'\"\"%F&F,F&F&*(\"#5F&)F'F)F&)F,F*F&F&*(F7F&)F'F*F&)F,F)F&F& *(F.F&F'F&)F,F5F&F&*$)F,F.F&F&!\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*.^#\"#;\"\"\"\"\"##F&F'%(kappa2|irG#\"\"&F'%\"eGF&%(kappa1|irG#\" \"$F',.*$)F-F+F&F&*(F+F&)F-\"\"%F&F)F&F&*(\"#5F&)F-F/F&)F)F'F&F&*(F7F& )F-F'F&)F)F/F&F&*(F+F&F-F&)F)F5F&F&*$)F)F+F&F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 353 "int(int(int(conjugate(psi100n)*e*r*cos(t heta)*psi21m1n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi) ;\nint(int(int(conjugate(psi100n)*e*r*sin(theta)*cos(phi)*psi21m1n*r^2 *sin(theta),r=0..infinity),phi=0..2*Pi),theta=0..Pi);\nint(int(int(con jugate(psi100n)*e*r*sin(theta)*sin(phi)*psi21m1n*r^2*sin(theta),r=0..i nfinity),phi=0..2*Pi),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"#;\"\"\"%(kappa1|irG# \"\"$\"\"#%\"eGF&%(kappa2|irG#\"\"&F*F*#F&F*,.*$)F'F.F&F&*(F.F&)F'\"\" %F&F,F&F&*(\"#5F&)F'F)F&)F,F*F&F&*(F7F&)F'F*F&)F,F)F&F&*(F.F&F'F&)F,F5 F&F&*$)F,F.F&F&!\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*.^#!#;\"\" \"\"\"##F&F'%(kappa2|irG#\"\"&F'%\"eGF&%(kappa1|irG#\"\"$F',.*$)F-F+F& F&*(F+F&)F-\"\"%F&F)F&F&*(\"#5F&)F-F/F&)F)F'F&F&*(F7F&)F-F'F&)F)F/F&F& *(F+F&F-F&)F)F5F&F&*$)F)F+F&F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "r1 := int(int(int(conjugate(psi100n)*e*r*sin(theta)* cos(phi)*psi21m1n*r^2*sin(theta),r=0..infinity),phi=0..2*Pi),theta=0.. Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r1G,$*.\"#;\"\"\"%(kappa1|i rG#\"\"$\"\"#%\"eGF(%(kappa2|irG#\"\"&F,F,#F(F,,.*$)F)F0F(F(*(F0F()F) \"\"%F(F.F(F(*(\"#5F()F)F+F()F.F,F(F(*(F9F()F)F,F()F.F+F(F(*(F0F(F)F() F.F7F(F(*$)F.F0F(F(!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "r2 := subs(kappa2=kappa1/2,r1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#r2G,$**\"$G\"\"\"\"\"$V#!\"\"%(kappa1|irGF*%\"eGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "subs(kappa1 = m0*e^2/(4*Pi*epsilon0 *hbar^2),r2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*0\"$7&\"\"\"\"$V#! \"\"%#m0GF(%\"eGF(%#PiGF&%)epsilon0GF&%%hbarG\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }