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Interaction energy in small N ‐particle systems and the permutation group
Author(s) -
Holas A.,
Działak H.,
Olszewski S.
Publication year - 1988
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.560340307
Subject(s) - antisymmetric relation , representation theory of the symmetric group , symmetric group , permutation group , permutation (music) , irreducible representation , degenerate energy levels , wave function , coulomb , perturbation theory (quantum mechanics) , physics , mathematics , group (periodic table) , interaction energy , quantum mechanics , young tableau , identical particles , combinatorics , mathematical physics , electron , molecule , acoustics , quantum
The distribution of energy levels of an N ‐identical‐particle system among the irreducible representations of the permutation group is examined for a “spin‐free” problem. There are calculated the sums of powers of the eigenenergies obtained from the original N !‐fold degenerate energy level when the interaction between the particles is switched on. The first‐order perturbation theory is applied. Some results of the present approach are shown to be equivalent to the results of the Weyl's theory of the permutation group. The distribution of energy levels is found to be symmetric with respect to the average energy level belonging to a self‐conjugate representation. For a special case of the Coulomb interaction the wave function of the highest level is fully symmetric, whereas that of the lowest level is fully antisymmetric with respect to the interchange of the coordinates of any two particles. The average energy and the dispersion of the levels belonging to a given representation are calculated for some N .