We assume that
Schrödinger equation is transformed in recurrences by a suitable power series ansatz
and boundary conditions are proved equivalent to a vanishing Hill determinant
(= finite-dimensional at a "reference" or "zero-order" coupling g_0).
On a particular double-well polynomial-potential illustration
we demonstrate that:
unperturbed propagators may be made triangular,
their diagonally dominated form supports convergence of intermediate summations,
perturbation corrections for energies are easy to construct and
perturbation series appears better convergent than the HD method itself.
Published in Phys. Lett. A 150 (1990) 67 - 69 and
Phys. Lett. A 222 (1996) 291 - 298.