We propose a new version of the multipoint Pade technique to solve Sch
rodinger equations in their first-order Riccati form. Our compact prod
uct representation of wavefunctions interpolates or 'matches' availabl
e approximants at several points. The mechanism of 'matching' determin
es the energies and eliminates spurious solutions. On V(x) = mu(2) x(2
) + lambda x(2)/(1 + gx(2)), its efficiency is illustrated numerically
.