  Disordered systems have grown in importance in the past decades, with similar
phenomena manifesting themselves in many different physical systems. Because of
the difficulty of the topic, theoretical progress has mostly emerged from
numerical studies or analytical approximations. Here, we provide an exact,
analytical solution to the problem of uniform phase disorder in a system of
identical scatterers arranged with varying separations along a line. Relying on
a relationship with Legendre functions, we demonstrate a simple approach to
computing statistics of the transmission probability (or the conductance, in
the language of electronic transport), and its reciprocal (or the resistance).
Our formalism also gives the probability distribution of the conductance, which
reveals features missing from previous approaches to the problem.
