A note about the mixed regularity of Schrödinger Coulomb system
Meng, Long (2019), A note about the mixed regularity of Schrödinger Coulomb system. https://basepub.dauphine.fr/handle/123456789/20332
TypeDocument de travail / Working paper
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We give a short and unified proof of mixed regularity of Coulomb system for several cases: antisymmetric case with order of derivatives smaller than 1.25 which is the best bound; mixture of antisymmetry and non-antisymmetry with order of derivatives 1+β and α respevtively for 0≤0<α<0.75, 0.75<β<1.25 and α+β<1.5 which is also the oprtimal bound; and purely non-antisymmetric case with order of derivatives up to 0.75. In addition to Hardy type inequality, it is based on the Herbst inequality. Such results are of particular importance for the study of sparse grid-like expansions of the wavefunctions. Moreover, we can get how fast the norm of these derivative can increase with the number of electrons.
Subjects / KeywordsSchrödinger Coulomb system
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