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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 161 "This worksheet  shows how
 the probability density function of a free particle develops over tim
e. I recommend that you use Classic Worksheet Maple to execute it." }}
{PARA 0 "" 0 "" {TEXT -1 54 "Arham Amouie Foumani, 22 February 2008 (3
 Esfand 1386)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assume(p0,
real);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assume(x,real);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assume(m,real);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assume(t,real);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "assume(hbar,real);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "Psi(x,t):=1/sqrt(2*Pi*hbar)*int(ex
p(-(p-p0)^2)*exp(I/hbar*(p*x-1/2*p^2/m*t)),p=-infinity..infinity):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Psi2(x,t):=simplify(abs(Psi
(x,t))^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dispexp:=eval
(Psi2(x,t),\{m=1,p0=7,hbar=1.055e-34\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "interface(warnlevel=0):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 180 "animate(plot,[dispexp,x=-5..70,y=-1..2,title=\"Time development
 of free particle's probability density function\",labels=[\"x\",\"pro
bability density\"]],t=0..10,frames=100,thickness=2);" }{TEXT -1 0 "" 
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