 
Summary: ARTICLES
Two interacting electrons in a box: An exact diagonalization study
Ali Alavia)
School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom and
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
Received 31 May 2000; accepted 17 August 2000
The behavior of two electrons confined to a threedimensional box with infinite walls and interacting
with a Coulomb potential is studied using an exact diagonalization technique. The use of symmetry
operators enables the Hamiltonian to be block diagonalized. Apart from the total spin, the
wavefunctions can be classified using three symmetry quantum numbers. The Coulomb integrals are
shown to be amenable to efficient and accurate calculation. The energy of the lowest few eigenstates
of both the singlet (S 0) and triplet (S 1) are calculated as a function of the box size i.e., in
effect rs) for a slightly tetragonally distorted box where the zaxis is longer than the x and yaxes.
The ground state is a singlet function with ggg symmetry at all densities. At small rs , the ground
state has a maximum in electron density at the box center. Upon increasing rs , at rs 8 a.u., the
ground state density acquires a minimum in the box center. At this same rs , the firstexcited state
of the singlet manifold changes its symmetry from ggu to ugu, and the corresponding degeneracy
is changed from one to two. The energyrs curve shows a nonanalytic change in slope. Subsequent
increasing of rs gives rise to increased localization of the charge density in the eight corners of the
box, which can be identified as the ``Wigner'' crystal limit of the present model. The physical
