  The aim of the present paper is to clarify the relationship between
immersions of surfaces and solutions of the inhomogeneous Dirac equation. The
main idea leading to the description of a surface M^2 by a spinor field is the
observation that the restriction to M^2 of any parallel spinor phi on R^3 is
(with respect to the inner geometry of M^2) a non-trivial spinor field on M^2
of constant length which is a solution of the inhomogeneous Dirac equation and
vice versa.
