  Quantum theory is formulated as the uniquely consistent way to manipulate
probability amplitudes. The crucial ingredient is a consistency constraint: if
the amplitude of a quantum process can be computed in two different ways, the
two answers must agree. The constraint is expressed in the form of functional
equations the solution of which leads to the usual sum and product rules for
amplitudes. An immediate consequence is that the Schrodinger equation must be
linear: non-linear variants of quantum mechanics violate the requirement of
consistency.
  PACS: 03.65.Bz, 03.65.Ca.
