In quantum physics it is well known that two observables

and

* * can be incompatible, with

*.* These are represented by

* *noncommutating Hermitian operators:

*. *As a consequence, the uncertainties

* *and

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 position

* *and is valid for each quantum state.

[1] P. Meystre and M. Sargent III,

*Elements of Quantum Optics*, New York: Springer–Verlag, 1991.

[2] M. O. Scully and M. S. Zubairy,

*Quantum Optics*, Cambridge: Cambridge University Press, 1997.