  We consider the applicability of phase space Wannier functions" to electronic
structure calculations. These generalized Wannier functions are analogous to
localized plane waves and constitute a complete, orthonormal set which is
exponentially localized both in position and momentum space. Their properties
are described and an illustrative application to bound states in one dimension
is presented. Criteria for choosing basis set size and lattice constant are
discussed based on semi-classical, phase space considerations. Convergence of
the ground state energy with respect to basis size is evaluated. Comparison
with plane-waves basis sets indicates that the number of phase space Wannier
functions needed for convergence can be signicantly smaller in three
dimensions. PACS: 71.10.+x, 71.50.+t
