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===Visualization=== The uncertainty principle can be visualized using the position- and momentum-space wavefunctions for one spinless particle with mass in one dimension. The more localized the position-space wavefunction, the more likely the particle is to be found with the position coordinates in that region, and correspondingly the momentum-space wavefunction is less localized so the possible momentum components the particle could have are more widespread. Conversely, the more localized the momentum-space wavefunction, the more likely the particle is to be found with those values of momentum components in that region, and correspondingly the less localized the position-space wavefunction, so the position coordinates the particle could occupy are more widespread. These wavefunctions are [[Fourier transform]]s of each other: mathematically, the uncertainty principle expresses the relationship between conjugate variables in the transform. [[File:Quantum mechanics travelling wavefunctions wavelength.svg|center|thumb|502px|Position ''x'' and momentum ''p'' wavefunctions corresponding to quantum particles. The colour opacity of the particles corresponds to the [[probability density]] of finding the particle with position ''x'' or momentum component ''p''.<br/> '''Top:''' If wavelength ''Ξ»'' is unknown, so are momentum ''p'', wave-vector ''k'' and energy ''E'' (de Broglie relations). As the particle is more localized in position space, Ξ''x'' is smaller than for Ξ''p<sub>x</sub>''.<br/> '''Bottom:''' If ''Ξ»'' is known, so are ''p'', ''k'', and ''E''. As the particle is more localized in momentum space, Ξ''p'' is smaller than for Ξ''x''.]] {{Clear}}
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