4 problems

Let $H_N$ be the $N$-electron atomic Hamiltonian with nuclear charge $Z\in\mathbb{N}$, and let $E_N=\inf\sigma(H_N)$. Denote by $N_c=N_c(Z)$ the largest number of electrons for whi…

Let an atomic nucleus have charge $\mu$, and let the number of electrons bound to it be the quantity under consideration. Ionization conjecture. The number of electrons that can be…

Let $Z$ be the atomic number of an atom. For a molecule, let $K$ be the number of nuclei and let $Z$ be its total nuclear charge. Maximum excess-charge conjecture. An atom of atomi…

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…