I am trying to solve the Schrodinger equation:
-y''(x) = (E-V(x))*y(x),
where the potential V(x) is not known in quadratures. The potential V(x) comes from numerical solution of ODE, and is known only a discrete set of points and given by the vector [V(x_1), V_(x_2), ...], and has the following plot:
So, the question is: what is the best way to solve this problem? (apart from the obvious choice to fit the data and solve the equation with the fitted potential)