In quantum physics it is well known that two observables
can be incompatible, with .
These are represented by
noncommutating Hermitian operators: .
As a consequence, the uncertainties
do not vanish simultaneously;
denotes the variance of the operator
. The variances depend on the actual state of the physical system. Therefore, no quantum state
exists for the physical system considered with and .
As an example, the Heisenberg uncertainty relation
follows from the quantum commutation relation of the noncommutating operators momentum
and is valid for each quantum state.
 P. Meystre and M. Sargent III, Elements of Quantum Optics
, New York: Springer–Verlag, 1991.
 M. O. Scully and M. S. Zubairy, Quantum Optics
, Cambridge: Cambridge University Press, 1997.