Update to v1.0:
Through rewrite, almost from scratch, with a new emphasis on positive x.
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set ylabel "$|\\psi|^2$" norotate
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set xlabel "$\\frac{t\\omega}{2\\pi}$"
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#
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## start ticks at 0, then every x
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set xtics 0,1
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#set ytics 0,1
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set xrange [0:3]
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# default output canvas size: 12.5cm x 8.75cm
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set term lua tikz size 8,6 standalone
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# no key
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set key off
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# set linestyle
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set style line 1 linetype rgbcolor "#4169E1" linewidth 3
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set style line 2 linetype rgbcolor "#DC143C" linewidth 3
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set style line 3 linetype rgbcolor "#32CD32" linewidth 3
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set style line 4 linetype rgbcolor "#4B0082" linewidth 3
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set style line 5 linetype rgbcolor "#000000" linewidth 1
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set pointsize 0.6
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plot \
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 "x2.dat" using 1:2 with lines linestyle 2 ,\
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 "x4.dat" using 1:2 with lines linestyle 3 ,\
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 "x6.dat" using 1:2 with lines linestyle 4
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