  We 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.
