  We offer a clear physical explanation for the emergence of the quantum
operator formalism, by revisiting the role of the vacuum field in quantum
mechanics. The vacuum or random zero-point radiation field has been shown
previously, using the tools of stochastic electrodynamics, to be central in
allowing a particle subject to a conservative binding force to reach a
stationary state of motion. Here we focus on the stationary states, and
consider the role of the vacuum as a driving force. We observe that the
particle responds resonantly to certain field modes. A proper Hamiltonian
analysis of this response allows us to unequivocally trace the origin of the
basic quantum commutator, by establishing a one-to-one correspondence between
the response coefficients of x and p and the respective matrix elements. The
(random) driving field variables disappear thus from the description, but their
Hamiltonian properties become embodied in the operator formalism. The
Heisenberg equations establish the dynamical relationship between the response
functions.
