物理學(xué)院“博約學(xué)術(shù)論壇”系列報告第22期     (2012年第11期)

The original formulation of the uncertainty relation by Heisenberg, which is based on a thought experiment with an emphasis on measurement processes, lacked a simple mathematical basis compared to the widely accepted relations of Kennard and Robertson. In fact, a naive form of the Heisenberg-type relation has been recently invalidated by experiment. On the other hand, the analysis of measurement processes was missing in the relations of Kennard and Robertson. In this paper we reformulate the Heisenberg uncertainty relation in such a manner that it incorporates both of the intrinsic quantum fluctuations and the effects of measurement, and yet with the same mathematical basis as the relations of Kennard and Robertson and thus universally valid. This relation, which assumes the form $/Delta x/Delta p/sim /hbar$ (instead of $/hbar/2$) when written in a popular notation, is regarded as a combination of the past works on the uncertainty relation by Arthurs and Kelly, who emphasized the role of measurement apparatus, and by Ozawa who clarified the mathematical structure.