Figure 38-13 shows a case in which the momentum component

Chapter , Problem 69

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Figure 38-13 shows a case in which the momentum component px of a particle is fixed so that )px ! 0; then, from Heisenbergs uncertainty principle (Eq. 38-28), 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 l/2p, where l is the particles 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 12p?