For the electronic Schrödinger equation, Yserentant has recently shown that solution wavefunctions possess bounded mixed weak derivatives. This makes it worthwhile to explore the benefit of sparse grid or hyperbolic cross techniques to solve equations of this type.

Sparse grid methods exhibit a substantially lower complexity with respect to the problem dimension than conventional discretization techniques. Furthermore there exists a dimension-adaptive sparse grid variant which adaptively determines important problem dimensions and thus further reduces the dependence of the complexity from the dimension of the problem under consideration.

We consider the use of sparse grids for Schrödinger type equations and investigate possible applications. For simple examples, we study the feasibility and problems of the dimension-adpative sparse grid approach. To this end, we use a method which is similar to the pseudospectral technique which combines the sparse grid advantages of a tensor product construction between single and pair subspaces and adaptive multiresolution bases for the evaluation of the potential function within these low-dimensional subspaces.