| Abstract:
I present a new collocation method for solving the Schroedinger equation. Col-
location has the advantage that is obviates integrals. Previous collocation methods have, however,
all had the crucial disadvantage that they require solving a generalized eigenvalue problem. By
combining Lagrange-like functions with a Smolyak interpolant we device a collocation method that
does not require solving a generalized eigenvalue problem. We exploit the structure of the basis
and the grid to develop an efficient algorithm for evaluating the matrix-vector products required
to compute energy levels and wavefunctions. Energies systematically converge as the number of
points and basis functions is increased.
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