On the Energy of a Large Atom
نویسندگان
چکیده
We announce a proof of an asymptotic formula for the groundstate energy of a large atom. The early work of Thomas-Fermi, Hartree-Fock, Dirac, and Scott predicted that for an atomic number Z , the energy is E(Z) « -cQZ ^ + c{Z 2 c2Z 513 for known c0, cx, and c2 (see [5]). Schwinger [7] observed an additional effect and set down the modified formula E(Z) « -cQZ ' +cxZ •yC2Z . Our proof shows that Schwinger's formula is correct. We give the precise formulation of the problem. For a fixed nucleus of charge Z and quantized electrons x{, . . . , xN e R , the Hamiltonian HN z is the self-adjoint operator
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