  The Schroedinger operator on the Newtonian space-time is defined in a way
which is independent on the class of inertial observers. In this picture the
Schroedinger operator acts not on functions on the space-time but on sections
of certain one-dimensional complex vector bundle over space-time. This bundle,
constructed from the data provided by all possible inertial observers, has no
canonical trivialization, so these sections cannot be viewed as functions on
the space-time. The presented framework is conceptually four-dimensional and
does not involve any ad hoc or axiomatically introduced geometrical structures.
It is based only on the traditional understanding of the Schroedinger operator
in a given reference frame and it turns out to be strictly related to the
frame-independent formulation of analytical Newtonian mechanics that makes a
bridge between the classical and quantum theory.
