In
quantum physics, the outcome of even an ideal
measurement of a system is not
deterministic, but instead is characterized by a
probability distribution, and the larger the associated
standard deviation is, the more "uncertain" we might say that that characteristic is for the system. The
Heisenberg uncertainty principle, or HUP, gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible to have a particle that has an arbitrarily well-defined position and momentum simultaneously. More precisely, the product of the standard deviations , where is the
reduced Planck constant. The principle generalizes to many other pairs of quantities besides position and momentum (for example, angular momentum about two different axes), and can be derived directly from the
axioms of quantum mechanics.
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Heisenberg's uncertainty principle; Heisenberg principle.The exact momentum and exact location of a particle cannot be specified. Werner Heisenberg stated that the product of uncertainties in location and momentum measurements can never be smaller than h/4 , where h is
Planck's constant .