A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain, and show that by utilizing the implications of the Quantum Recurrence Theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss

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... iefly the possibility of using these results in the control of infinite dimensional coupled harmonic oscillators, and also draw attention to some of the issues and open questions arising from this and related work.