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2011

Uncertainty relation for photons

Bialynicki-Birula, Iwo, Bialynicka-Birula, Zofia

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Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics.

The photon energy density plays the role of the probability density in configuration space.
It is shown that the measure of the spatial extension based on the energy distribution in space combined with a measure of the spread in the photon momentum leads to an inequality that is a natural counterpart of the standard Heisenberg relation.
Unexpectedly, the equation satisfied by the photon wave function in momentum space which saturates the uncertainty relations has the form of the Schr\"odinger equation in coordinate space in the presence of electric and magnetic charges.

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Then

A. F. Rañada and J. L. Trueba, Phys. Lett. A 202
1995
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I. Bialynicki-Birula, Photon wave function Progress in Optics
1996
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A. F. Rañada and J. L. Trueba, Nature 383
1996
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K. A. Milton, G. R. Kalbfleisch, Wei Luo, and L. Gamberg, Intl. J. Mod. Phys. A 17
2002
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I. Bialynicki-Birula, J. Opt. A: Pure Appl. Opt. 6
2004
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A. S. Holevo, Rep. Math. Phys. 13
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K. A. Milton, Rep. Prog. Phys. 69
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