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Coulomb Hamiltonian

A Coulomb Hamiltonian is a many-particle Schroedinger operator with pair interactions proportional to reciprocal distance. For N electrons with two spin states and fixed distinct nuclei at R_j in R^3 with charges Z_j>0, its atomic-unit form is

H_N=sum_(i=1)^N(-1/2Delta_i-sum_(j=1)^M(Z_j)/(|x_i-R_j|))+sum_(i<k)1/(|x_i-x_k|).

It acts on the antisymmetric space ^ ^(N)L^2(R^3;C^2). A fixed nuclear repulsion term may be added without affecting successive-electron energy differences. Write E_N=infsigma(H_N) and Z=sum_(j)Z_j. Strict binding of the Nth electron means E_N<E_(N-1).

See also

Ground State, Ionization Conjecture, Kohn-Sham Representability, QMA, Schrödinger Operator, Thomas-Fermi Model

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References

Penz, M.; Tellgren, E. I.; Csirik, M. A.; Ruggenthaler, M.; and Laestadius, A. "The Structure of the Density-Potential Mapping. Part I: Standard Density-Functional Theory." ACS Phys. Chem. Au 3, 334-347, 2023. https://doi.org/10.1021/acsphyschemau.2c00069.Solovej, J. P. "The Ionization Conjecture in Hartree-Fock Theory." Ann. Math. 158, 509-576, 2003. https://doi.org/10.4007/annals.2003.158.509.

Cite this as:

Weisstein, Eric W. "Coulomb Hamiltonian." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CoulombHamiltonian.html

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