BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Solving the Schrodinger equation using Smolyak interpolants Avilla, Gustavo


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.

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