  This paper examines how best to associate quantum states of a single particle
to different modes of a narrowly collimated beam of classical radiation modeled
in the paraxial approximation. Our analysis stresses the importance of the
relationship between two inner products naturally arising in the problem. These
are the inner product used to expand a general beam as a superposition of
orthogonal modes in the paraxial approximation, on the one hand, and the
canonical inner product on which the statistical interpretation of quantum
(field) theory is founded, on the other. While several candidates for the sort
of association between beam modes and single-particle quantum states have been
proposed in the literature, here we argue that one of them is uniquely well
suited to the task. Specifically, the mapping of beam modes to the
``henochromatic'' quantum states previously introduced by Sudarshan, Simon and
Mukunda is unique within a large class of similar mappings in that it is
unitary in a mathematically precise sense.
