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( Uncertainty principle)
Mathematical formulation of... In quantum physics, the Heisenberg uncertainty principle states that the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both be known with arbitrary precision. That is, the more precisely one variable is known, the less precisely the other is known. This is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but rather about the nature of the system itself. In quantum mechanics, the particle is described by a wave. The position is where the wave is concentrated and the momentum, a measure of the velocity, is the wavelength. The position is uncertain to the degree that the wave is spread out, and the momentum is uncertain to the degree that the wavelength is ill-defined. The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there are no states which describe a particle with both a definite position and a definite momentum. The narrower the probability distribution is for the position, the wider it is in momentum.
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