The mathematics of large atoms
The spin of the ground state of an atom.
In this paper we address a question posed by M. and T. Hoffmann-Ostenhof, which concerns the total spin of the ground state of an atom or molecule. Each electron is given a value for spin, ±1/2. The total spin is the sum of the individual spins.
Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.
In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potential VTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of ⎧ y''(x) = x-1/2y3/2(x), ⎨ y(0) =...
Weyl sums and atomic energy oscillations.
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
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