  We investigate the relation between the invariant operators satisfying the
quantum Liouville-von Neumann and the Heisenberg operators satisfying the
Heisenberg equation. For time-dependent generalized oscillators we find the
invariant operators, known as the Ermakov-Lewis invariants, in terms of a
complex classical solution, from which the evolution operator is derived, and
obtain the Heisenberg position and momentum operators. Physical quantities such
as correlation functions are calculated using both the invariant operators and
Heisenberg operators.
