**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.**