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Sparse grid spaces for the numerical solution of the electronic Schrödinger equation. (English) Zbl 1084.65125
This paper is concerned with the approximate solution of the electronic Schrödinger equation that is used to model the molecular behaviour of some particle systems in quantum mechanics. The author presents some results that complement his recent publication [Numer. Math. 98, 731–759 (2004; Zbl 1062.35100)] by proposing suitable sets of sparse grid trial functions so that the dimension of the trial spaces is reduced to a tractable level. An extensive bibliography that is relevant for the problem under consideration is also included.

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J10 Schrödinger operator, Schrödinger equation
35B65 Smoothness and regularity of solutions to PDEs
35Q40 PDEs in connection with quantum mechanics
81P05 General and philosophical questions in quantum theory
81V25 Other elementary particle theory in quantum theory
Full Text: DOI
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