TY - JOUR
T1 - Two electrons on a hypersphere
T2 - A quasiexactly solvable model
AU - Loos, Pierre François
AU - Gill, Peter M.W.
PY - 2009/9/18
Y1 - 2009/9/18
N2 - We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a D-sphere (D≥1), is a polynomial in the interelectronic distance u for a countably infinite set of values of the radius R. A selection of these radii and the associated energies are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the D=3 model bears the greatest similarity to normal physical systems.
AB - We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a D-sphere (D≥1), is a polynomial in the interelectronic distance u for a countably infinite set of values of the radius R. A selection of these radii and the associated energies are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the D=3 model bears the greatest similarity to normal physical systems.
UR - http://www.scopus.com/inward/record.url?scp=70349283032&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.103.123008
DO - 10.1103/PhysRevLett.103.123008
M3 - Article
SN - 0031-9007
VL - 103
JO - Physical Review Letters
JF - Physical Review Letters
IS - 12
M1 - 123008
ER -