  A previous one-dimensional derivation of Schr\"odinger's equation from
statistical assumptions is generalized to three spatial dimensions, gauge
fields, and spin. It is found that the same statistical assumptions that imply
Schr\"odinger's equation determine also the form of the gauge coupling terms,
and the form of the corresponding local (Lorentz) forces. An explanation for
the role of the electrodynamic potentials, as statistical representatives of
the Lorentz force, is given. Spin one-half is introduced as the property of a
statistical ensemble to respond to an external gauge field in two different
ways. A generalized calculation, using the twofold number of variables, leads
to Pauli's equation. The new spin term is again the statistical representative
of the corresponding local force. The classical limit $\hbar \to 0$ of
Schr\"odinger's equation and closely related questions of interpretation of the
quantum mechanical formalism are discussed.
