Supersymmetric quantum mechanics is discussed in the spaces of one and three dimensions. The structure of the continuum portion of the spectrum of the hamiltonian is investigated by making use of Callias' and Weinberg's generalized index theorems. The difference of the densities of bosonic and fermionic states at a fixed energy is calculated and it turns out to be topologically invariant and non­ vanishing in the presence of continuous spectra. Supersymmetric quantum mechanics (SQM) is the simplest supersymmetric model invented by Witten!) to envisage how the dynamical breakdown of super symmetry takes place. He considered SQM whose energy spectrum consisted only of discrete levels. He defined a convenient quantity which is now called Witten's index. 2 )