  Sufficient conditions for complete controllability of $N$-level quantum
systems subject to a single control pulse that addresses multiple allowed
transitions concurrently are established. The results are applied in particular
to Morse and harmonic-oscillator systems, as well as some systems with
degenerate energy levels. Morse and harmonic oscillators serve as models for
molecular bonds, and the standard control approach of using a sequence of
frequency-selective pulses to address a single transition at a time is either
not applicable or only of limited utility for such systems.
