  A simple model of quantum particle is proposed in which the particle in a
{\it macroscopic} rest frame is represented by a {\it microscopic
d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The
state vectors are defined simply by complex combinations of coordinates and
momenta. It is argued that the observables of the system are Hermitian forms
(corresponding uniquely to Hermitian matrices). Quantum measurements transforms
the equilibrium state obtained after preparation into a family of equilibrium
states corresponding to the critical values of the measured observable
appearing as values of a random quantity associated with the observable. Our
main assumptions state that: i) in the process of measurement the measured
observable tends to minimum, and ii) the mean value of every random quantity
associated with an observable in some state is proportional to the value of the
corresponding observable at the same state. This allows to obtain in a very
simple manner the Born rule.
