The authors discuss the time evolution of a one-dimensional supersymmetric quantum mechanical system, in which the supersymmetry is broken by an additional potential. The potentials under consideration belong to a special class and can be in general time dependent. They analyse the special case of time-independent potentials and have used the Jaynes-Cummings model in (1963) quantum optics as a simple example in their analysis. For the time dependent potentials, they use the basic evolution operator technique developed by C M Cheng and P C W Fung and present a way in which to treat such problems.