The uncertainties (root-mean-square deviations), indicated by Δ, satisfy the inequalities ![]() The best-known canonically conjugate pairs for which Heisenberg's uncertainty relations are valid are the components of position r = ( x, y, z) and of momentum p = ( p x, p y, p z) of a particle. Even when a quantum mechanical system is in a well-defined state, a pair of its canonically conjugate properties cannot be determined simultaneously with arbitrary certainty. ![]() In quantum mechanics, the Heisenberg uncertainty relations, named after their discoverer Werner Heisenberg, state that pairs of certain physical quantities cannot be measured simultaneously with arbitrarily small error.
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