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Solving the Schrodinger equation using Smolyak interpolants

Banff International Research Station for Mathematical Innovation and Discovery

Interpolation on sparse grids using the Smolyak idea has been used to compute the vibrational levels of CH2O. The complete Watson kinetic energy operator was used. Standard collocation methods require solving a generalized eigenvalue problem, HU=SUE. If the basis is large solving a generalized eigenvalue problem is much more costly than solving HU=UE. The interpolation method we use requires solving HU=UE, but H is not symmetric. Like other sparse grid methods it overcomes the “curse of the dimensionality”. The accuracy of the energies depends both on the functions used to interpolate and on the interpolation points. We choose good interpolating functions because, according to the Boys’ theorem, this will reduce error in the energies.

Mathematics; Quantum theory; Partial differential equations; Mathematical physics

video/mp4

Author affiliation: Queen's University

2014-08-06

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49351

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/