We discuss spatial grid methods adapted to the structure of Hilbert spaces,
used to simulate quantum mechanical systems. We review the construction of
Finite Basis Representation (FBR) and the Discrete Variable Representation
(DVR). A mixed representation (pseudo-spectral method) is constructed thro
ugh a quadrature relation linking both bases. (C) 1999 Elsevier Science B.V
. All rights reserved.