Phase‐Space Versus Coordinate‐Space Methods: Prognosis for Large Quantum Calculations

This chapter provides a simple pedagogical presentation of the discrete variable representation (DVR). It reviews the von Neumann (vN) basis of phase‐space Gaussians which include the Projected von Neumann Basis (PvN) and the Biorthogonal von Neumann Basis (PvB). The chapter includes a variety of interesting formal properties of nonorthogonal bases that are an extension of the DVR presentation and provides insight into the method. It presents an analysis of multidimensional considerations, including details of a highly efficient tensor formulation for performing pruned multidimensional DVR calculations for sparse but unstructured grids. The chapter contains illustrative applications. Pruned phase‐space methods have been successfully used for computing eigenenergies of (ro‐) vibrational systems. The chapter focuses on the applications in the context of solving the time‐dependent Schrodinger equation (TDSE). The efficiency of phase‐space versus coordinate‐space methods will certainly depend on the particular system studied and the strength of coupling between degrees of freedom.