New approach to the correlation problem: Electron interaction potential as a variable in solving the many-particle Schrödinger equation
- 47 Downloads
The many-electron wave function is represented as the product of the wave function of the independent particles and the function that depends only on the value of the interelectron interaction potential. The function defines the electron correlation effects; a standard linear differential equation was derived to define the function. The equation depends on the functions of independent particles; a generalization of the Hartree-Fock equations including electron correlation was obtained for these functions. The total energy calculation of two-electron ions shows that even solving an ordinary differential equation for the function of independent particles represented by the functions of noninteracting electrons leads to higher accuracy than the one achieved in the Hartree-Fock theory.
Keywordselectron-electron correlations ionization energies of helium-like ions generalized Hartree-Fock equations
- 5.L. D. Landau and E. M. Livshits, Quantum Mechanics [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
- 6.P. Gombash, Many-Particle Problem in Quantum Mechanics [in Russian], Inostrannaya Literatura, Moscow (1953).Google Scholar
- 7.S. K. Godunov and V. S. Ryabenkii, Difference Schemes [in Russian], Nauka, Moscow (1977).Google Scholar
- 8.H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One-and Two-Electron Atoms, Springer, Berlin (1957).Google Scholar