  Heisenberg introduced his famous uncertainty relations in a seminal 1927
paper entitled "The Physical Content of Quantum Kinematics and Mechanics". He
motivated his arguments with a gedanken experiment, a gamma ray microscope to
measure the position of a particle. A primary result was that, due to the
quantum nature of light, there is an inherent uncertainty in the determinations
of the particle's position and momentum dictated by an indeterminacy relation,
$\delta q \delta p \sim h$. Heisenberg offered this demonstration as "a direct
physical interpretation of the [quantum mechanical] equation $\textbf{pq} -
\textbf{qp} = -i\hbar$" but considered the indeterminacy relation to be much
more than this. He also argued that it implies limitations on the very meanings
of position and momentum and emphasized that these limitations are the source
of the statistical character of quantum mechanics. In addition, Heisenberg
hoped but was unable to demonstrate that the laws of quantum mechanics could be
derived directly from the uncertainty relation. In this paper, we revisit
Heisenberg's microscope and argue that the Schr\"odinger equation for a free
particle does indeed follow from the indeterminacy relation together with
reasonable statistical assumptions.
