An iterative solution of Schrodinger's equation

The energy function E( lambda ) of a quantum system with Hamiltonian H( lambda )=H₀+ lambda H₁ is determined by an analytical iterative procedure which yields a rich variety of functional forms. The wavefunction iterates include the solutions of Rayleigh-Schrodinger perturbation theory as well as some additional functions, all of which may be obtained sequentially by standard analytical techniques. At each step, an arbitrary ( lambda -dependent) constant may be chosen freely so as to improve the results of low-order iterates, thereby enhancing the convergence of the procedure.