Heisenberg Uncertainty Product for Different Photon States

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.

References

[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.

[3] J. J. Sakurai, Modern Quantum Mechanics, Reading, MA: Addison–Wesley, 1995.