The quantum $N$ -electron structure problem is expressed as a classical $N$ -body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using $k$ -electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory $(k=1)$ and pair density-functional theory $(k=2)$ and culminating in an exact treatment of the entire $N$ -electron system $(k=N)$ .The quantum $N$-electron structure problem is expressed as a classical $N$-body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using $k$-electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory $(k=1)$ and pair density-functional theory $(k=2)$ and culminating in an exact treatment of the entire $N$-electron system $(k=N)$.

Physical Review AOct 3, 200644 citations

The Many-electron Problem

Elsevier eBooksJan 1, 19720 citations

Interaction of an alkaline-earth atom with an electron: scattering, negative ion and photodetachment

G. F. Gribakin, B. V. Gul'tsev, V. K. Ivanov +1 more

Three mutually related problems concerning the interaction of an electron with an alkaline-earth atom are examined. (i) The scattering problem: the phaseshifts for p-electron scattering by Ca, Sr and Ba are calculated. (ii) The negative ion problem: the wavefunction and the binding energy are obtained for the outer electron in Ca - 4s 2 4p, Sr - 5s 2 5p and Ba - 6s 2 6p ions. (iii) The photodetachment problem: the photodetachment cross sections are calculated for the outer electron in each of these ions. The most intriguing feature of these problems is the strong correlational potential, attracting the electron to the atom due to the large dipole polarizabilities of Ca, Sr and Ba. The calculations are performed by means of the Dyson equation of the many-body theory.Three mutually related problems concerning the interaction of an electron with an alkaline-earth atom are examined. (i) The scattering problem: the phaseshifts for p-electron scattering by Ca, Sr and Ba are calculated. (ii) The negative ion problem: the wavefunction and the binding energy are obtained for the outer electron in Ca - 4s 2 4p, Sr - 5s 2 5p and Ba - 6s 2 6p ions. (iii) The photodetachment problem: the photodetachment cross sections are calculated for the outer electron in each of these ions. The most intriguing feature of these problems is the strong correlational potential, attracting the electron to the atom due to the large dipole polarizabilities of Ca, Sr and Ba. The calculations are performed by means of the Dyson equation of the many-body theory.

Journal of Physics B Atomic Molecular and Optical PhysicsDec 28, 199079 citations

The many-electron problem

K. S. Viswanathan

Asia Pub. House eBooksJan 1, 19661 citation

(p,q)-Sheaves and the Representability Problem

A. I. Panin

General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.

arXiv:physics/0210070Oct 18, 20020 citations

MANY-ELECTRON FUNCTION

WORLD SCIENTIFIC eBooksFeb 19, 20190 citations

The quantum

N

-electron structure problem is expressed as a classical

N

-body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using

k

-electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory

(k=1)

and pair density-functional theory

(k=2)

and culminating in an exact treatment of the entire

N

-electron system

(k=N)