General Decomposition of Radial Functions on R^n and Applications to N-Body Quantum Systems

Details General Decomposition of Radial Functions on R^n and Applications to N-Body Quantum Systems General Decomposition of Radial Functions on R^n and Applications to N-Body Quantum Systems

2001-07-11

arxiv.org/abs/math-ph/0107011v2

Lett. Math. Phys. 61, 75 (2002)

Physics

Mathematical Physics

revised and extended version; to appear in Lett. Math. Phys

Scientific paper

We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions $V$ on $R^n$ going to zero at infinity. This generalized decomposition can be used to extend previous results on $N$-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.

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