We find the largest convex minorant of the function ¶ \begin{equation*} F\left( x,y\right) =ax^{2}+xy+by^{2} \end{equation*} ¶ where $a,b$ are positive constants and $x\geq 0,\ y\geq 0$. We explain how the problem is closely connected with\ finding the ground state Thomas-Fermi electron density for a spin\ polarized quantum mechanical system with the Fermi-Amaldi correction.
Convex minorant, Thomas-Fermi theory, Fermi-Amaldi correction, ground state electron density, 52A41, 26B25, 81Q99, 81V55, 92E10
Convex minorant, Thomas-Fermi theory, Fermi-Amaldi correction, ground state electron density, 52A41, 26B25, 81Q99, 81V55, 92E10
We find the largest convex minorant of the function ¶ \begin{equation*} F\left( x,y\right) =ax^{2}+xy+by^{2} \end{equation*} ¶ where $a,b$ are positive constants and $x\geq 0,\ y\geq 0$. We explain how the problem is closely connected with\ finding the ground state Thomas-Fermi electron density for a spin\ polarized quantum mechanical system with the Fermi-Amaldi correction.