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Electron diffraction

Continuing with our analysis of experiments that lead to the new quantum theory, we now look at the phenomenon of electron diffraction. It is well-known that light has the ability to diffract around objects in its path, leading to an interference pattern that is particular to the object. This is, in fact, how holography works (the interference pattern is created by allowing the diffracted light to interfere with the original beam so that the hologram can be viewed by shining the original beam on the image). A simple illustration of diffraction is the Young double slit experiment pictured below:

Figure: From www.lightandmatter.com
\includegraphics[scale=1.0]{double-slit-wave.eps}
Here, we use water waves (pictured as waves in a plane parallel to the double slit apparatus) and observe what happens when they impinge on the slits. Each slit then becomes a point source for spherical waves that subsequently interfere with each other, giving rise to the light and dark fringes on the screen at the bottom. The intensity of the fringes is depicted in the sketch below:
Figure: From hyperphysics.phy-astr.gsu.edu
\includegraphics[scale=1.0]{dslit.eps}

If laser light is used, the interference pattern appears as shown below:

Figure 3:
\includegraphics[scale=2.0]{Laserdiffraction.eps}
Amazingly, if electrons are used instead of light in the double-slit experiment, and a fluorescent screen is used, one finds the same kind of interference pattern! This is shown in the electron double-slit diffraction pattern below:
Figure 4: From zms.desy.de
\includegraphics[scale=1.0]{electron_double_slit.eps}
Obviously, classical mechanics is not able to predict such a result. If the electrons are treated as classical particles, one would predict an intensity pattern corresponding to particles that can pass through one slit or the other, landing on the screen directly opposite the slite (i.e., no intensity maximum at the center of the screen):
Figure 5: Intensity pattern for ``classical'' electrons
\includegraphics[scale=0.5]{classical_electron_dslit.eps}

The width of each peak is a direct measure of the width of the slits. Since, in classical mechanics, the electrons follow definite, deterministic, predictable paths, there an be no deviation from this pattern. For this reason, the classical explanation cannot be the correct one.



We will consider two different rationalizations of the electron double-slit experiment.



Subsections
next up previous
Next: Particle-wave picture Up: lecture_5 Previous: lecture_5
Mark E. Tuckerman 2011-12-12