5 problems

Let a negative atomic ion be described by a non-relativistic many-particle Hamiltonian whose nuclear charge varies as a parameter, and let the nuclear charge be critical when the l…

Let hydrogen and antihydrogen interact through pure Coulomb forces. Hydrogen–antihydrogen bound-state conjecture. No bound state of the hydrogen–antihydrogen system exists. The pap…

Strong Scott conjecture. The suitably rescaled ground-state density $\rho_S$ on distances of order $Z^{-1}$ from the nucleus converges to $\rho_S^H$, equivalently to $q$ times the…

Let $E_S(N,Z)$ denote an eigenvalue of the relevant many-particle Coulomb Hamiltonian, where $N$ is the number of electrons and $Z$ the nuclear charge. Ionization conjecture. There…

Let $\mu^{(\beta, W, \theta)}_{n_1,n_2}$ denote the Gibbs measures for the quasi-one-dimensional Coulomb system with inverse temperature $\beta$, width parameter $W$, boundary phas…