  Toy models of a non-associative quantum mechanics are presented. The
Heisenberg equation of motion is modified using a non-associative commutator.
Possible physical applications of a non-associative quantum mechanics are
considered. The idea is discussed that a non-associative algebra could be the
operator language for the non-perturbative quantum theory. In such approach the
non-perturbative quantum theory has observables and unobservables quantities.
