QUANTUM-MECHANICS IN THE E(1-VERTICAL-BAR-2) SUPERSPACE

Quantum mechanics in the E(1\2) superspace is presented and its differ ences with the super symmetric quantum mechanics, proposed by Witten, are exhibited. For central potential, the problem has an osp(1\2) symm etry which allows us to sepal ate odd Grassmann variables by means of the dispin basis, and to derive a radial equation. This equation is so lved in two cases: for the Coulomb potential bound states, where the e nergy levels ape the same as for the hydrogen atom, and for the isotro pic harmonic oscillator, where they ape translated. In both cases the energy levels are degenerated, but the states are labelled by the eige nvalues of the superspin and of the spin. The Fock space of the oscill ator is constructed.