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 Lagrangelike 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 matrixvector products required
to compute energy levels and wavefunctions. Energies systematically converge as the number of
points and basis functions is increased.
