5 problems

Let $H_a$ be the radial Coulomb–Dirac Hamiltonian … with $a,c<0$, and suppose that the positive-angular-parameter case $\kappa>0$ is under consideration. The point spectrum of…

Let $\triangle$ be a triangle with vertices $A$, $B$, and $C$. For a point $X$ in its plane, let $Q(X)$ be the triple of normalized stationary charges for which the gradient of the…

Optimality for a delta. The first eigenvalue is minimal when the charge distribution is concentrated at the origin, namely when $\mu=\mu(\mathbb{R}^3)\delta_0$. Equivalently, for a…

Let $M\geqslant2$, let $R_1,\ldots,R_M\in\mathbb{R}^3$ be nuclear positions, and let $\nu_1,\ldots,\nu_M\geqslant0$ be nuclear charges. Write … for the molecular energy, where the…

Let $D_0$ denote the free Dirac operator, let $ubinom{}{}$ be a nonnegative maximal total charge, and define … Here $\overline{\nu}_1$ is the critical coupling constant satisfying…