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A previous derivation of the single-particle Schr\"odinger equation fromstatistical assumptions is generalized to an arbitrary number $N$ of particlesmoving in three-dimensional space. Spin and gauge fields are also taken intoaccount. It is found that the same statistical assumptions that implySchr\"odinger's equation determine also the form of the gauge coupling terms,and the form of the corresponding local (Lorentz) forces. An explanation forthe role of the electrodynamic potentials, as statistical representatives ofthe Lorentz force, is given. For a single particle, spin one-half is introducedas the property of a statistical ensemble to respond to an external gauge fieldin two different ways. A generalized calculation, using the twofold number ofvariables, leads to Pauli's equation. The new spin term is again thestatistical representative of the corresponding local force. For a $N$-particlesystem, spin is introduced as a consequence of gauge coupling.The classicallimit $\hbar \to 0$ of Schr\"odinger's equation and closely related questionsof interpretation of the quantum mechanical formalism are discussed.

A statistical derivation of non-relativistic quantum theory