TWO-DIMENSIONAL ELECTRON GAS IN A PERIODIC POTENTIAL AND EXTERNAL MAGNETIC FIELD: STATES OF PAIRS AND THREE-PARTICLE SYSTEMS |
| W. Florek Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland |
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| Received: November 20, 2000 |
| The group-theoretical classification of states of identical particle pairs is presented. Then obtained states are coupled with those of an antiparticle to construct states of a three-particle system. Investigations are performed using products of irreducible projective representations of the 2D translation group. For a given Born-von Karman period N degeneracy of pair states is N, whereas three-particle states are N2-fold degenerated. It has to be underlined that the case of even N is more complicated since pair states are labelled by four inequivalent irreducible projective representations. The problem of symmetry properties with respect to particles transposition is briefly discussed. |
| DOI: 10.12693/APhysPolA.99.601 PACS numbers: 73.20.Dx, 71.70.Di, 02.20.-a |