Abstract
A MOST elegant demonstration of the uncertainty relation for two real observables A and B has been given by Born1. Let us denote mean values with a bar, and assume the linearity condition 
with a, b real constants, is satisfied for every two real operators M and N. Assume also 
where D = M + iN, D* = M − iN.
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References
See, for example, Born, M., “Natural Philosophy of Cause and Chance”, 189 (Oxford, 1949).
Gamba, A., N. Cim., 7, 378 (1950).
Schrödinger, E., Sitz. Preuss. Akad., 296 (1930).
Reed, Ronald L., and Dresden, M., Bull. Amer. Phys. Soc., 25, 3 (1950).
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GAMBA, A. The Uncertainty Relation. Nature 166, 653–654 (1950). https://doi.org/10.1038/166653a0
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DOI: https://doi.org/10.1038/166653a0
