N = 4 Supersymmetric Morse Oscillator andIts Spectrum-Generating Algebra**The projectsupported by National Natural Science Foundation of Chinaunder Grant No. 10275038, and partly by the State Key BasicResearch Development Program under Grant No. G2000077400,and Natural Science Foundation of Tsinghua University

Abstract

In this paper N = 4 supersymmetry of generalized Morse oscillators inone dimension is studied. Both bound states and scattering states of its foursuperpartner Hamiltonians are analyzed by using unitary irreducible representationsof the noncompact Lie algebra su(1,1).The spectrum-generating algebra governing the Hamiltonian of the N = 4supersymmetric Morse oscillator is shown to be connected with the realization of Liesuperalgebra osp(1,2) or B(0,1) in terms of the variables ofa supersymmetric two-dimensional harmonic oscillator.