  A notion of rational Baker-Akhiezer (BA) function related to a configuration
of hyperplanes in C^n is introduced. It is proved that BA function exists only
for very special configurations (locus configurations), which satisfy certain
overdetermined algebraic system. The BA functions satisfy some algebraically
integrable Schrodinger equations, so any locus configuration determines such an
equation. Some results towards the classification of all locus configurations
are presented. This theory is applied to the famous Hadamard's problem of
description of all hyperbolic equations satisfying Huygens' Principle. We show
that in a certain class all such equations are related to locus configurations
and the corresponding fundamental solutions can be constructed explicitly from
the BA functions.
