σ = 0.2; n0 = 40;
k0 = N[π];

Clear[x, y, n, Fo, Fe, ψo, ψe, ψ];
\(\(\(ϕo[x_, n_]\)\(=\)\(Sin[n*π*x/2]\)\(
\)\)\)
\(ϕe[x_, n_] = Cos[n*π*x/2]
\)
\(ψ0[
        y_] = \(\(\((2*π*σ^2)\)^\((\(-1\)/
              4)\)\)\(*\)\(Exp[\(\(-y^2\)/2\)/σ^2 + 
            I*k0*y]\)\(
\)\)\)
\(\(Fo[n_] := 
        NIntegrate[ϕo[y, n]*ψ0[y], {y, \(-1\), 1}];\)
\)
\(\(Fe[n_] := 
        NIntegrate[ϕe[y, n]*ψ0[y], {y, \(-1\), 1}];\)
\)
\(\(ψo[x_, t_] := 
        Sum[ϕo[x, n]*coefo[\([n]\)]*Exp[\(-I\)*n^2*t], {n, 2, n0, 
            2}];\)
\)
\(\(ψe[x_, t_] := 
        Sum[ϕe[x, n]*coefe[\([n]\)]*Exp[\(-I\)*n^2*t], {n, 1, n0, 
            2}];\)
\)
ψ[x_, 
          t_] := ψo[x, t] + ψe[x, 
            t];

coefe  =  Table[Fe[n], {n, 1, n0}];
\(\(coefo\  = \ Table[Fo[n], {n, 1, n0}];\)

\)

g0 = 
      Plot[Abs[ψ0[x]]^2, {x, -1, 1}, Frame -> True, 
        PlotRange -> All];

g = 
        Table[Plot[Abs[ψ[x, t]]^2, {x, -1, 1}, Frame -> True, 
            PlotPoints -> 14,  PlotRange  ->  {0, 2}],  {t, 0.02, 
            1.0, 0.02}];

plot1 = Show[GraphicsArray[gg]];

Display["fig1.eps", plot1, "EPS"];

Plot

gp = {g0}; Do[gp = Append[gp, g[[i]]], {i, 1, 9}];

gpa = 
      Table[Show[gp[[i]], PlotRange -> {0, 2}, Axes -> False], {i, 1, 
          Dimensions[gp][[1]]}];

gg = 
      Table[{gpa[[i]], gpa[[i + 1]]}, {i, 1, 
          Dimensions[gpa][[1]]/2}];

plot2 = Show[GraphicsArray[gg]];

Display["fig2.eps", plot2, "EPS"];