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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 28 "K\351tpontos perem\351rt
\351k feladat" }{TEXT -1 1 "\n" }{TEXT 257 31 "1D potenci\341l  k\366t
\366tt \341llapotai\n" }}{PARA 19 "" 0 "" {TEXT 261 30 "Bog\341r Feren
c\n2002. m\341rcius 27." }}{PARA 0 "" 0 "" {TEXT 262 2 " \n" }{TEXT 
258 37 "Az  y''+2(e-v)y=0 egyenlet megold\341sa." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 18 "R\351szecske dobozban" }
}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Proced\372r\341k" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart:\nwith(plots):" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 "#In
tegr\341l\341s balr\363l jobbra \nbox:=proc(e)\nlocal dsys,init,balrol
,val;\ndsys := diff(y(x),x,x)+2*e*y(x)=0;\ninit:= y(0)=0,D(y)(0)=1;\ns
ol := dsolve(\{dsys,init\},\{y(x)\},numeric,start=0);\nval:=op(2,sol(1
)[2]);\nval\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 264 "boxprint:=pro
c(e)\nlocal dsys,init,balrol,box;\ndsys := diff(y(x),x,x)+2*e*y(x)=0;
\ninit:= y(0)=0,D(y)(0)=1;\nbalrol := dsolve(\{dsys,init\},\{y(x)\},nu
meric,start=0);\nbox:=odeplot(balrol,[x,y(x)],0..1,labels=[x,y],\n    \+
        numpoints=50,color=blue):\ndisplay(box);\nend:" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT 260 35 "Pr\363b\341ljunk ki k\374l\366nb\366z
\365 energi\341kat!" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "etry:=3:\nboxprint(etry);" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 25 "Keress\374nk saj\341t\351rt\351keket!" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 390 "#Set parameters\n toler:=0.000001;\n e1:
=200;\n f1:=box(e1):\n e2:=e1+2*toler:\n dd:=100:\n# Find eigenvalue\n
  for delt while dd > toler do;  \n   f2:=box(e2);\n   f21:=f2-f1;dd:=
abs(e2-e1);\n   if abs(f21) > 0 and dd > toler then;\n    enext:=e1+f1
*(e1-e2)/f21;\n    e1:=e2;f1:=f2;e2:=enext;\n   else\n    dd:=toler/2;
\n   fi;\n  od:\n# Result\n print('e', e2);\n evalf([i^2*Pi^2/2 $i=1..
6]);\n boxprint(e2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
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1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }