  The dynamics of states representing arbitrary N-level quantum systems,
including dissipative systems, can be modelled exactly by the dynamics of
classical coupled oscillators. There is a direct one-to-one correspondence
between the quantum states and the positions of the oscillators. Quantum
coherence, expectation values, and measurement probabilities for system
observables can therefore be realized from the corresponding classical states.
The time evolution of an N-level system is represented as the rotation of a
real state vector in hyperspace, as previously known for density matrix states
but generalized here to Schrodinger states. A single rotor in n dimensions is
then mapped directly to n oscillators in one physical dimension. The number of
oscillators needed to represent N-level systems scales linearly with N for
Schrodinger states, in contrast to N^2 for the density matrix formalism.
Although the well-known equivalence (SU(2), SO(3) homomorphism) of 2-level
quantum dynamics to a rotation in real, physical space cannot be generalized to
arbitrary N-level systems, representing quantum dynamics by a system of coupled
harmonic oscillators in one physical dimension is general for any N. Values for
the classical coupling constants are readily obtained from the system
Hamiltonian, allowing construction of classical mechanical systems that can
provide visual insight into the dynamics of abstract quantum systems as well as
a metric for characterizing the interface between quantum and classical
mechanics.
