Invariants of motion for an N-level system

For an N-level system interacting with N-1 laser fields, it is shown that there exist in general N2-N+1 independent invariants of motion when the Hamiltonian assumes a time-independent form under a suitable unitary transformation. Two different procedures to obtain these invariants are presented. The special case of N=3 is considered in detail and two new independent invariants are shown to exist in addition to the five already known. Explicit expressions for these two invariants are also given.