BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Seré DTSTART:20210614T133000Z DTEND:20210614T143000Z DTSTAMP:20260423T024023Z UID:MCQM21/1 DESCRIPTION:Title: D irac-Coulomb operators with general charge distribution: results and open problems\nby Eric Seré as part of Mathematical Challenges in Quantum Mechanics 2021 Workshop\n\n\nAbstract\nThis talk is based on joint works w ith M.J. Esteban and M. Lewin. Consider an electron moving in the attracti ve Coulomb potential generated by a non-negative finite measure representi ng an external charge density. If the total charge is fixed\, it is well k nown that the lowest eigenvalue of the corresponding Schrodinger operator is minimized when the measure is a delta. We investigate the conjecture th at the same holds for the relativistic Dirac-Coulomb operator. First we gi ve conditions ensuring that this operator has a natural self-adjoint reali sation and that its eigenvalues are given by min-max formulas. Then we def ine a critical charge such that\, if the total charge is fixed below it\, then there exists a measure minimising the first eigenvalue of the Dirac-C oulomb operator. Moreover this optimal measure concentrates on a compact s et of Lebesgue measure zero. The last property is proved using a new uniqu e continuation principle for Dirac operators.\n LOCATION:https://researchseminars.org/talk/MCQM21/1/ END:VEVENT END:VCALENDAR