 The Born rule states that an observable property of a quantum system is defined by a Hermitian operator on a separable Hilbert space , that the only observable values of the property are the eigenvalues of the operator , and that the probability of the system being observed in a particular eigenvalue is the square of the absolute value of the complex number obtained by projecting the state vector ( a point in the Hilbert space ) onto the corresponding eigenvector . George Mackey had asked whether Born 's rule is a necessary consequence of a particular set of axioms for quantum mechanics , and more specifically whether every measure on the lattice of projections of a Hilbert space can be defined by a positive operator with unit trace . Though Richard Kadison proved this was false for two @-@ dimensional Hilbert spaces , Gleason 's theorem ( published 1957 ) shows it to be true for higher dimensions . 
