By Ira N. Levine
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Then photons will bounce off each electron as it passes the slits and will be observed through the microscope. The observer thus can tell through which slit each electron has passed, and also record its ﬁnal position on the phosphorescent screen. In this experiment, it is necessary to use light having a wavelength short in comparison to the interslit distance; otherwise the microscope cannot resolve a ﬂash well enough to tell which slit it is nearest. When this experiment is performed, we indeed detect each electron as coming through one slit or the other, and not both, but we also ﬁnd that the diffraction pattern on the screen has been lost and that we have the broad, featureless distribution shown in Fig.
034 × 1022 cm−1 . Clearly, this is light of an extremely short wavelength since more than 1022 wavelengths ﬁt into 1 cm. 000 eV, the above equation is repeated using h in eV s. This gives ν˜ = 8065 cm−1 . 1-7 The Wave Nature of Matter Evidently light has wave and particle aspects, and we can describe it in terms of photons, which are associated with waves of frequency ν = E/ h. Now photons are rather peculiar particles in that they have zero rest mass. In fact, they can exist only when traveling at the speed of light.
But what about the next point, x = L + 2 dx, and all the other points outside the box? If we try to use the same device, we end up with the requirement that ψ be nonsmooth at every point where V = ∞. A function that is 27 28 Figure 2-1 Chapter 2 Quantum Mechanics of Some Simple Systems The potential felt by a particle as a function of its x coordinate. , a continuous f cannot be 100% corners. To have recognizable corners, we must have some (continuous) edges. ) Hence, if V = ∞ at a single point, we might ﬁnd a solution ψ which is ﬁnite at that point, with ﬁnite energy.