2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185982We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire functions (L and K) and the zeroes of K are identical to those of the wave function. Requiring such a zero at a large but finite value of the argument yields the low energy eigenstates with exponentially small errors. Judicious choice of G can improve dramatically the numerical treatment. The method yields many significant digits with modest computer means.10 pages, 8 figures, uses revtex; new section added, references addedQuantum PhysicsHigh Energy Physics - TheoryMathematical PhysicsComputational Physicstext