DAN Yuya    Department   Matsuyama University  Department of Business Administration, Faculty of Business Administration    Position   Professor
Language	English
Publication Date	2014/08
Type
Peer Review	With peer review
Title	Riesz means of bound states for Schrödinger operators
Contribution Type
Journal	SEOUL ICM 2014, International Congress of Mathematicians
Publisher	SC11-03-01, Mathematical Physics
Details	The energy of ground states for quantum complex systems with the electromagnetic interaction can be determined from the spectrum calculated for the Schrödinger operator. It has been proven that the Riesz mean of all negative energies for the Hamiltonian is bounded with good coefficients. Lieb and Thirring conjectured that the coefficient in the inequalities should coincide with the semi-classical one according to the Thomas-Fermi model. Now, the refinement of the coefficients shown in 2008 by Dolbeault, Laptev and Loss is believed to be best possible. On the other hand, Rumin and Solovej showed another approach for a derivation of the Lieb-Thirring coefficient in 2011. The main result is to propose a sufficient condition for the Lieb-Thirring conjecture according to the method by Rumin-Solovej.