Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems

Details Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems

2007-09-05

arxiv.org/abs/0709.0565v1

Commun.Math.Phys.280:545-562,2008

Physics

Mathematical Physics

17 pages; to appear in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-008-0450-4

A Schroedinger type equation on the superspace R^{D|2n} is studied, which involves a potential inversely proportional to the negative of the osp(D|2n) invariant "distance" away from the origin. An osp(2,D+1|2n) dynamical supersymmetry for the system is explicitly constructed, and the bound states of the system are shown to form an irreducible highest weight module for this superalgebra. A thorough understanding of the structure of the irreducible module is obtained. This in particular enables the determination of the energy eigenvalues and the corresponding eigenspaces as well as their respective dimensions.

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