Mathematical and Numerical Methods for Complex Quantum Systems

Efficient spectral Galerkin methods for electronic structure calculations

Yingwei Wang

Purdue University


In quantum chemistry the main interest is to find an approximation to the solution of the Schrodinger equation, which is a high-dimensional eigenvalue problem. In this work, we propose efficient spectral Galerkin methods for one-dimensional electronic Schrodinger equations. Furthermore, we apply the Slalter determinant which gives antisymmetric grids, suited to fermionic systems. Besides, the Galerkin discretization results in a generalized linear eigenvalue problem, which is solved by the trace minimization scheme. Several numerical experiments are presented to show the costs, accuracy and convergence rates with respect to the number of electrons in the system.