Orthosymplectic Lie Superalgebras in Superspace Analogues of Quantum Kepler Problems

A Schrödinger type equation on the superspace $\mathbb {R}^{D|2n}A Schr?dinger type equation on the superspace 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.