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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "This worksheet shows a sim
ulation of the wavefunctions in an infinite square well (i.e. a one-" 
}}{PARA 0 "" 0 "" {TEXT -1 103 "dimensional box extending from x=0 to \+
x=a).  For plotting purposes, the variable x/a is a dimensionless" }}
{PARA 0 "" 0 "" {TEXT -1 105 "x and 2*Pi*hbar*t/E1, in which E1 is the
 energy of the ground state, is a dimensionless time t.  Use this" }}
{PARA 0 "" 0 "" {TEXT -1 111 "worksheet as follows.  Enter a combinati
on of coefficients for the first 4 stationary states of the system int
o" }}{PARA 0 "" 0 "" {TEXT -1 102 "the array c1.  This prepares a wave
function that is a superposition of these 4 states.  The next steps" }
}{PARA 0 "" 0 "" {TEXT -1 106 "create a normalized set of coefficients
 c2.  Psi1 is the general solution to the 1-d particle in a box for" }
}{PARA 0 "" 0 "" {TEXT -1 102 "superpositions of the first 4 stationar
y states.  The two animations that follow show the real part of" }}
{PARA 0 "" 0 "" {TEXT -1 106 "the wavefunction and the probability dis
tribution as they develop in time.  Enjoy.  Incidentally, the real" }}
{PARA 0 "" 0 "" {TEXT -1 96 "part of Psi1 is exactly the solution to a
 vibrating violin string with only 3 overtones present." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "c1 := array(1..4,[5,4,3,2]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c1G-%'VECTORG6#7&\"\"&\"\"%\"\"$\"
\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "c2 := array(1..4,[])
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c2G-%&arrayG6$;\"\"\"\"\"%7\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "den:= sqrt(sum(c1[i]^2,
i=1..4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$denG,$*$\"\"'#\"\"\"\"
\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "for j from 1 to
 4 do c2[j] := evalf(c1[j]/den) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>&%#c2G6#\"\"\"$\"+w\"QT!o!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#
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\"$$\"+1H[#3%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#c2G6#\"\"%$\"+
q_l@F!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "Psi1 := unapply( evalf(sqr
t(2.0)*sum( c2[i]*sin(i*Pi*x)*exp(-I*i^2*2*Pi*t),i=1..4)),x,t);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Psi1G:6$%\"xG%\"tG6\"6$%)operatorG%
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