Energy eigenvalue level motion and a SymbolicC plus plus implementation

We consider the Hamilton operator (H) over cap(epsilon) = (H) over cap (0) + epsilon(V) over cap. We assume that (H) over cap(epsilon) has a discrete spectrum. We show that the energy eigenvalues and eigenvectors obey an auto nomous system of ordinary differential equations. An implementation of this system of differential equations is given using SymbolicC++.