Supersymmetric dynamical invariants

We address the problem of identifying the (nonstationary) quantum systems t hat admit supersymmetric dynamical invariants. In particular, we give a gen eral expression for the bosonic and fermionic partner Hamiltonians. Due to the supersymmetric nature of the dynamical invariant the solutions of the t ime-dependent Schrodinger equation for the partner Hamiltonians can be easi ly mapped to one another. We use this observation to obtain a class of exac tly solvable time-dependent Schrodinger equations. As applications of our m ethod, we construct classes of exactly solvable time-dependent generalized harmonic oscillators and spin Hamiltonians.