  The foundations of non-linear quantum mechanics are based on six postulates
and five propositions. On a first quantised level, these approaches are built
on non-linear differential operators, non-linear eigenvalue equations, and the
notion of non-linear observables and non-linear states. The present theory
predicts that the non-linear function solution of a non-linear partial
differential equation for a free particle is correct and that the commutator of
the position operator and the non-linear momentum operator does not commute.
Moreover, the implicit wave function of linear quantum mechanics can be
determined by a non-linear wave function solution of non-linear partial
differential equation, which also verifies the non-linear quantum mechanics.
