Numerically integrate the time of two oscillatory functions from NDEigensystem.

The mathematica code goes like this:

L = 1000*10^-10; F = 10^7; m = 0.0665*9.1*10^-31; mhole = 0.34*9.1*10^-31; e = 1.6*10^-19; [HBar] = 1.05*10^-34; Ne = 199; eqn1 = (-(\[HBar]^2/(2 m))* (\[Phi]^\[Prime]\[Prime])[x] + e*F*x*\[Phi][x]); eqn2 = (-(\[HBar]^2/(2 mhole))* (\[Psi]^\[Prime]\[Prime])[x] - e*F*x*\[Psi][x]) {phivals, phifuns} = NDEigensystem[{eqn1, DirichletCondition[\[Phi][x] == 0, x \[GreaterSlantEqual] L/2 || x <= -L/2]}, \[Phi][x], {x, -L/2, L/2}, Ne, Method -> {"SpatialDiscretization" ->{"FiniteElement", {"MeshOptions" -> {MaxCellMeasure -> 10^-9}}}}]; {psivals, psifuns} = NDEigensystem[{eqn2, DirichletCondition[\[Psi][x] == 0, x \[GreaterSlantEqual] L/2 || x <= -L/2]}, \[Psi][x], {x, -L/2, L/2}, Ne, Method -> {"SpatialDiscretization" -> "FiniteElement", \{"MeshOptions" -> {MaxCellMeasure -> 10^-9}}}}];