Abstract
The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in the field of clamped nuclei and forms the basis of quantum chemistry. The present article continues the author’s recent work (Numer. Math. 98, 731–759, 2004) on the regularity of its solutions, the electronic wavefunctions. It was shown in the mentioned article that these wavefunctions possess square integrable high-order mixed weak derivatives as they are needed to justify and underpin sparse grid and hyperbolic cross space approximation techniques theoretically. How fast the norms of these derivatives can increase with the number of electrons is studied in the present article. Provided that all quantities are properly related to a characteristic lengthscale of the considered atomar or molecular system, the norms of the derivatives remain bounded independent of the number of electrons and the number, the positions, and the charges of the nuclei.
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Yserentant, H. The hyperbolic cross space approximation of electronic wavefunctions. Numer. Math. 105, 659–690 (2007). https://doi.org/10.1007/s00211-006-0038-x
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DOI: https://doi.org/10.1007/s00211-006-0038-x