  Based on an analysis of two conventional preparators, the Stern-Gerlach and
the hole-in-the-screen ones, it is argued that four entities can be taken as
the basic ingredients of a rather general theory of a quantum preparator. These
are the composite-system (object plus preparator) state coming about as a
result of a suitable interaction between the subsystems, a suitable preparator
projector called the triggering event, the conditional quantum state (density
operator) of the quantum object coming about as a consequence of the occurrence
of the triggering event on the preparator, and, finally, a unitary evolution
operator of the object subsystem acting after preparation. The concepts of a
general conditional state and of retrospective apparent ideal occurrence (which
appears in the theory) are discussed in considerable detail. Ideal occurrence
and the selective L\"{u}ders formula, which are made use of, are reviewed.
Dynamical and geometrical preparators are distinguished in the general theory.
They are described by the same entities in the same way, but in terms of
different physical mechanisms from the point of view of standard interpretation
with collapse.
