![]() ![]() A nonzero function and its Fourier transform cannot both be sharply localized. Mathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding in are of one another (i.e., position and momentum are ). The picture of the uncertainty principle is more visually intuitive, but the more abstract picture formulates it in a way that generalizes more easily. Two alternative frameworks for quantum physics offer different explanations for the uncertainty principle. So it is helpful to demonstrate how it applies to more easily understood physical situations. ![]() The uncertainty principle is not readily apparent on the macroscopic scales of everyday experience. Note that the waves shown here are real for illustrative purposes only, whereas in quantum mechanics the wave function is generally complex. The Fourier transform is a mathematical operation that separates a wave packet into its individual plane waves. This wave packet becomes increasingly localized with the addition of many waves. ![]() The superposition of several plane waves to form a wave packet. ![]()
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