von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics

Starting with a time-independent Hamiltonian h and an appropriately chosen solution of the von Neumann equation i(rho) over dot(t)=[h,rho(t)] we construct its binary-Darboux partner h(1)(t) and an exact scattering solution of i(rho) over dot (1)(t)=[h(1)(t),rho(1)(t)], where h(1)(t) is time dependent and not isospectral to h. The method is analogous to supersymmetric quantum mechanics but is based on a different version of a Darboux transformation. We illustrate the technique by the example where h corresponds to a one-dimensional harmonic oscillator. The resulting h(1)(t) represents a scattering of a solitonlike pulse on a three-level system.