  We show that the Schr\"{o}dinger equation for the quantum harmonic oscillator
can be derived as an approximation to the Newtonian mechanics of a classical
harmonic oscillator subject to a random force for time intervals $O( m /
\hbar)$, when $\hbar / m \ll 1$. Conversely, every solution to the
Schr\"{o}dinger equation, including all the superposition states, arises this
way. In other words, the quantum harmonic oscillator is approximately nothing
but the classical harmonic oscillator, with the same mass and frequency as the
quantum harmonic oscillator, subject to a random force. We generalize the
result to multiple non-interacting oscillators. We show that the
Schr\"{o}dinger equation for $n$ non-interacting quantum harmonic oscillators
with masses $m_1, ..., m_n$ and frequencies $\omega_1, ..., \omega_n$ can be
derived as an approximation to the Newtonian mechanics of $n$ non-interacting
classical harmonic oscillators, with the same set of masses and frequencies as
the quantum oscillators, subject to random forces. This is valid for time
intervals $O( \tilde{m} / \hbar)$, where $\tilde{m}$ is the mass of the minimum
mass oscillator, when $\hbar/\tilde{m} \ll 1$. Conversely, every solution,
including all the entangled states, to the Schr\"{o}dinger equation arises this
way. In other words, $n$ non-interacting quantum harmonic oscillators are
approximately nothing but $n$ non-interacting classical harmonic oscillators,
with the same set of masses and frequencies as the quantum oscillators, subject
to random forces. This provides a local Newtonian model of entanglement of
non-interacting quantum oscillators. The correlations required by entangled
states are embedded in the phase space probability density of the classical
oscillators.
