  The wave function of quantum mechanics is not a boost invariant and gauge
invariant quantity. Correspondingly, reference frame dependence and gauge
dependence are inherited to most of the elements of the usual formulation of
quantum mechanics (including operators, states and events). If a frame
dependent and gauge dependent formalism is called, in short, a relative
formalism, then the aim of the paper is to establish an absolute, i.e., frame
and gauge free, reformulation of quantum mechanics. To fulfil this aim, we
develop absolute quantities and the corresponding equations instead of the wave
function and the Schr\"odinger equation. The absolute quantities have a more
direct physical interpretation than the wave function has, and the
corresponding equations express explicitly the independent physical aspects of
the system which are contained in the Schr\"odinger equation in a mixed and
more hidden form. Based on the absolute quantities and equations, events,
states and physical quantities are introduced also in an absolute way. The
formalism makes it possible to obtain some sharper versions of the uncertainty
relation and to extend the validity of Ehrenfest's theorem. The absolute
formulation allows wide extensions of quantum mechanics. To give examples, we
discuss two known nonlinear extensions and, in close detail, a dissipative
system. An argument is provided that the absolute formalism may lead to an
explanation of the Aharonov-Bohm effect purely in terms of the electromagnetic
field strength tensor. At last, on special relativistic and curved spacetimes,
absolute quantities and equations instead of the Klein-Gordon wave function and
equation are given, and their nonrelativistic limit is derived.
