  A new approach to find exact solutions to one--dimensional quantum mechanical
systems is devised. The scheme is based on the introduction of a potential
function for the wavefunction, and the equation it satisfies. We recover known
solutions as well as to get new ones for both free and interacting particles
with wavefunctions having vanishing and non--vanishing Bohm potentials. For
most of the potentials, no solutions to the Schr\"odinger equation produce a
vanishing Bohm potential. A (large but) restricted family of potentials allows
the existence of particular solutions for which the Bohm potential vanishes.
This family of potentials is determined, and several examples are presented. It
is shown that some quantum, such as accelerated Airy wavefunctions, are due to
the presence of non--vanishing Bohm potentials. New examples of this kind are
found and discussed.
