{VERSION 6 0 "IBM INTEL LINUX" "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 "" 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 "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 "" 11 12 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 }{PSTYLE "Maple Plo t" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "ho1 := diff(psi(x),x,x) = (alpha^2* x^2-beta)*psi(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ho1G/-%%diffG6 $-%$psiG6#%\"xG-%\"$G6$F,\"\"#*&,&*&)%&alphaGF0\"\"\")F,F0F6F6%%betaG! \"\"F6F)F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dsolve(ho1, p si(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$psiG6#%\"xG,&*(%$_C1G\" \"\"F'#!\"\"\"\"#-%+WhittakerMG6%,$*(\"\"%F-%&alphaGF-%%betaGF+F+#F+F4 *&)F'F.F+F5F+F+F+*(%$_C2GF+F'F,-%+WhittakerWGF1F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "plot(eval(WhittakerW(1/4/alpha*beta,1/4,x ^2*alpha)/x^(1/2), \{alpha=1, beta=1\}), x=-5..5);" }}{PARA 13 "" 1 " " {GLPLOT2D 456 456 456 {PLOTDATA 2 "6%-%'CURVESG6$7K7$$\"+)oCR&>!#7$ \"+44)*****!#57$$\"+vjuV))F*$\"+_*3'****F-7$$\"+1oNt:!#6$\"+\\Bw)***F- 7$$\"+v*QBE#F6$\"+S7W(***F-7$$\"+7LISOF6$\"+\"HwL***F-7$$\"+]wE=]F6$\" +;kT()**F-7$$\"+Dj>uxF6$\"+[l#)p**F-7$$\"++D,`5F-$\"+R;rW**F-7$$\"+N#) >/;F-$\"+#p^@()*F-7$$\"*(RQb@!\"*$\"+BIRq(*F-7$$\"+v:+:JF-$\"+9$>k_*F- 7$$\"*=>Y2%FZ$\"+TaR.#*F-7$$\"+![K56&F-$\"+24dv()F-7$$\"*yXu9'FZ$\"+oQ By#)F-7$$\"+N@;=sF-$\"+;(*e1xF-7$$\"*\\y))G)FZ$\"+F&RE4(F-7$$\"+bbOO$* F-$\"+E4AnkF-7$$\"+i_QQ5FZ$\"+Q9gKeF-7$$\"+@]tR6FZ$\"+5$zIA&F-7$$\"+!y %3T7FZ$\"+]gXHYF-7$$\"+3kh`8FZ$\"+9#31+%F-7$$\"+O![hY\"FZ$\"+yrn8MF-7$ $\"+4FEn:FZ$\"+S+KGHF-7$$\"+#Qx$o;FZ$\"+k!>k[#F-7$$\"+y)Qjx\"FZ$\"+.Z^ k?F-7$$\"+u.I%)=FZ$\"+sjL%p\"F-7$$\"+(pe*z?FZ$\"+oam\\6F-7$$\"+C\\'QH# FZ$\"+AMI,sF67$$\"+8S8&\\#FZ$\"+tiTZWF67$$\"+0#=bq#FZ$\"+1;ZtDF67$$\"+ 2s?6HFZ$\"+$etUW\"F67$$\"+IXaEJFZ$\"+j8>RvF*7$$\"+l*RRL$FZ$\"+H+6eQF*7 $$\"+`<.YNFZ$\"+X_,g=F*7$$\"+8tOcPFZ$\"+PFbH')!#87$$\"+\\Qk\\RFZ$\"+Q? *z4%Fdv7$$\"+p0;rTFZ$\"+\")3/n;Fdv7$$\"+lxGpVFZ$\"+n$*R`r!#97$$\"+!oK0 e%FZ$\"+l0azFFdw7$$\"+<5s#y%FZ$\"+Paly5Fdw7$$\"\"&\"\"!$\"+sJlEP!#:-%' COLOURG6&%$RGBG$\"*++++\"!\")$FbxFbxF]y-%+AXESLABELSG6$%\"xGQ!6\"-%%VI EWG6$;$!\"&FbxF`x%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ho2 := diff(psi(x),x,x) = (alpha^2*x^2)*psi(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ho2G/-%%diffG6$-%$psiG6#%\"xG-%\"$G 6$F,\"\"#*(F)\"\"\")%&alphaGF0F2)F,F0F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "psi_ho2 := dsolve(ho2, psi(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(psi_ho2G/-%$psiG6#%\"xG,&*(%$_C1G\"\"\"F)#F-\"\"#-%( BesselJG6$#F-\"\"%,$*(F/!\"\",$*$)%&alphaGF/F-F7F.F)F/F-F-F-*(%$_C2GF- F)F.-%(BesselYGF2F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "ds olve(\{ho2, psi(-infinity)=0\}, psi(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "limit(psi_ho2, x=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&limitG6$-%$psiG6#%\"xG/F*%)infinityG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "series(eval(rhs(psi_ho2), \{ _C1=0, _C2=1\}), x=infinity);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,*** \"\"#\"\"\"*&F&F&*&%#PiGF&,$*$)%&alphaGF%F&!\"\"#F&F%F.#F&F%-%$cosG6#, &*(F%F.F*F0%\"xGF%F&*&\"\")F.F)F&F&F&*&F&F&F6F.F0F.*&#\"\"$F8F&**F'F0F *#F.F%-%$sinGF3F&F9#\"\"&F%F&F.*&#\"$0\"\"$c#F&**F'F0F-!\"#F1F&F9#\"\" *F%F&F.-%\"OG6#*$)F9#\"#8F%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "eval(psi_ho2, \{_C1=1, _C2=0, alpha=1\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$psiG6#%\"xG*&F'#\"\"\"\"\"#-%(BesselJG6$#F*\"\"%*&^ #F)F*)F'F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "7 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }