arXiv subjects
Publications and source records attributed to M. Hoffmann-Ostenhof.
In this paper we prove three differenttypes of the so-called many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimesnion $d\neq 2$. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a soplenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.
We prove that the electronic density of atomic and molecular eigenfunctions is smooth away from the nuclei. The result is proved without decay assumptions on the eigenfunctions.
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.
We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a charactisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.