Regularity and Approximability of Electronic Wave Functions

By Harry Yserentant. 2010

144 citations recorded by the source corpus.

Subfields: Mathematical Physics, Physical and Theoretical Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3fe82499708c10d01ab08dee648f74d7cff40562

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In Mathematical Physics

In Physical and Theoretical Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

The geometry of algorithms using hierarchical tensors (2013, background): “, [7,8]) and circumvent the curse of dimensionality by approximating the solution in a much lower dimensional space.”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Für die Lösungen der stationären elektronischen Schrödingergleichung konnte Yserentant [111] hohe gemischte Regularität zeigen.”
Hyperbolic Cross Approximation (2016, background): “There is a large class of solutions of the electronic Schrödinger equation in quantum chemistry, which belong to Sobolev spaces with mixed regularity and, moreover, possess some additional Sobolev isotropic smoothness properties, see Yserentant’s recent lecture notes [411] and the references therein”
Regularity of Tensor Product Approximations to Square Integrable Functions (2011, background): “Recent work by Yserentant [15] has shown this in the context of the electronic Schrödinger equation in quantum chemistry.”
On tensor products of quasi-Banach spaces (2010, methodology): “To name only some examples we refer to the work of Yserentant [26], who showed that eigenfunctions of the electronic Schrödinger equation belong to certain tensor product Sobolev spaces.”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “For a detailed treatment of decay properties of eigenfunctions and of the above characterization of Σ, we refer to the monograph [2] and to [152]; concerning further qualitative results on the spectrum of electronic Schrödinger operators, see also [126].”
Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods (2011, unknown): “6.1 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.2 Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140”