  We construct a tridiagonal matrix representation of the wave operator that
maps the wave equation into a three-term recursion relation for the expansion
coefficients of the wavefunction. Finding a solution of the recursion relation
is equivalent to solving the original problem. Consequently, a larger class of
solvable potentials is obtained. The usual diagonal representation constraint
results in a reduction to the conventional class of solvable potentials. To
exhibit the power of this approach, we give an exact solution for the infinite
potential well with sinusoidal bottom.
