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An SO(4) invariant Hamiltonian and the two‐body bound state. I: Coulomb interaction between two spinless particles
Author(s) -
Huntington Lee M. J.,
Nooijen Marcel
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.22206
Subject(s) - hamiltonian (control theory) , physics , bound state , euclidean space , mathematical physics , invariant (physics) , euclidean geometry , quantum mechanics , lie algebra , two body problem , coulomb , energy spectrum , quantum , mathematics , mathematical analysis , geometry , mathematical optimization , electron
We consider the nonrelativistic treatment of a hydrogenic atom in a four‐dimensional Euclidean space. The focus of this work is on the angular part of the problem, as this is potentially more generally applicable. Using a suitable coordinate system, the su(2)×su(2) structure of the so(4) Lie algebra is exploited. The hyperspherical harmonic solutions of the angular part of the problem are obtained in two ways: as solutions of a partial differential equation and by means of a ladder operator approach. The solutions of the radial equation and energy spectrum are determined and possible implications of the model are briefly discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009