Exact expression of the ground state energy of quantum many-particle systems as a functional of the particle density

Details Exact expression of the ground state energy of quantum many-particle systems as a functional of the particle density Exact expression of the ground state energy of quantum many-particle systems as a functional of the particle density

2001-01-29

arxiv.org/abs/cond-mat/0101428v1

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, latex file

Scientific paper

By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a two-dimensional electron gas under an external magnetic field, respectively. With the eigen-functionals of the particles, we can construct the ground state wave-function of the systems. Moreover, with the expressions of the ground state energy, we can exactly determine the ground state energy and the ground state particle density of the systems by taking $% \delta E_g[\rho ]/\delta \rho (x)=0$.

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