In a case in which the momentum component px of a particle is fixed so that...

In a case in which the momentum component px of a particle is fixed so that ?px = 0; then, from Heisenberg’s uncertainty principle (Eq. 38-20), the position x of the particle is completely unknown. From the same principle it follows that the opposite is also true; that is, if the position of a particle is exactly known (?x = 0), the uncertainty in its momentum is infinite. Consider an intermediate case, in which the position of a particle is measured, not to infinite precision, but to within a distance of ?/2?, where ? is the particle’s de Broglie wavelength. Show that the uncertainty in the (simultaneously measured) momentum component is then equal to the component itself; that is, ?px = p. Under these circumstances, would a measured momentum of zero surprise you? What about a measured momentum of 0.5p of 2p of l2p?

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genius_generous answered 2 years ago

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