Premium
An exact one‐electron model of the helium atom ground state
Author(s) -
Hunter Geoffrey,
Tai Chin Chiu
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560280817
Subject(s) - wave function , helium atom , physics , hartree–fock method , electron , ground state , schrödinger equation , quantum mechanics , electronic correlation , atomic physics , atom (system on chip) , quantum electrodynamics , computer science , embedded system
Expression of the Helium atom ground state wavefunction as a product of marginal and conditional factors together with averaging over the configuration space except for the distance of one electron from the nucleus, leads to a radial Schrödinger equation for the motion of one electron in an effective field produced by the nucleus and the other electron. The potential in this radial Schrödinger equation is in principle exact (i.e. it includes all of the correlation energy). Values of the potential are reported computed from correlated wavefunctions and from a Hartree‐Fock wavefunction; the correlated and Hartree‐Fock potentials are similar, the former being below the latter by and amount that averages to the correlation energy (0.04 a.u.). Thus Hartree's concept of a self‐consistent field for the motion of one electron is seen to be in principle exact. The exact theory has not, however, thus far yielded a set of simultaneous equations analogous with the Hartree‐Fock equations; the exact theory if a one‐electron model rather than an ab initio method for computing wave functions.