Solving the Schroedinger equation using Smolyak interpolants

Journal Article · Mon Oct 07 00:00:00 EDT 2013 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4821348· OSTI ID:22224137

Avila, Gustavo; Carrington, Tucker Jr. ^[1]

---

1. Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6 (Canada)

In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.

• OSTI ID: 22224137
• Journal Information: Journal of Chemical Physics, Vol. 139, Issue 13; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
ENERGY LEVELS
INTEGRAL EQUATIONS
INTERPOLATION
SCHROEDINGER EQUATION