分野別セミナー

The study of the electron distribution in atoms and molecules is paramount in quantum physics and chemistry. By
the uncertainty principle, the innermost electrons move with velocities which are a substantial fraction of the speed
of light. Hence, a relativistic description is mandatory. In the relativistic Chandrasekhar model, the electron
distribution close to the nucleus converges to the hydrogenic density, i.e., the sum of the squares of the
eigenfunctions of the single-particle Chandrasekhar operator. This confirms Elliott Lieb's strong Scott conjecture,
which was recently proved in joint work with Rupert Frank, Heinz Siedentop, and Barry Simon. In this talk, we
present new pointwise upper bounds for the hydrogenic density, in particular for each angular momentum channel
separately. Moreover, the upper bound is sharp for small distances. Our proof is concise and primarily relies on
recently established heat kernel bounds for Hardy perturbations of subordinated Bessel heat kernels. This talk is
based on joint works with Krzysztof Bogdan and Tomasz Jakubowski, and with Rupert Frank.