Young’s slits

An x-ray diffraction experiment is a very elaborate version of the Young s slit experiment. The regular layers of atoms in a crystal act as a three-dimensional collection of slits and give rise to a diffraction pattern that varies as the crystal is rotated and the slits are... 

Let us return to the Young s slits experiment (Fig. 1.4). Normally when this is performed, the quantum nature of light is not relevant. The intensity... 

Fig. 1.13 An Interference pattern, e.g. from the Young s slits experiment in Fig. 1.4, observed so that individual photons can be detected. The vertical scale shows the number of photons counted by each of a bank of 50 detectors. When only a few photons have arrived (a) they appear to be randomly distributed. As more come (b) and (c) the interference pattern predated by the wave Iheory emerges, but only as a statistical effect.

The essential features of the particle-wave duality are clearly illustrated by Young s double-slit experiment. In order to explain all of the observations of this experiment, light must be regarded as having both wave-like and particlelike properties. Similar experiments on electrons indicate that they too possess both particle-like and wave-like characteristics. The consideration of the experimental results leads directly to a physical interpretation of Schrodinger s wave function, which is presented in Section 1.8. 

Figure 1.8 Diagram of Young s double-slit experiment.

The wave interpretation of the interference pattern observed in Young s experiment is inconsistent with the particle or photon concept of light as required by Einstein s explanation of the photoelectric effect. If the monochromatic beam of light consists of a stream of individual photons, then each photon presumably must pass through either slit A or slit B. To test this assertion, detectors are placed directly behind slits A and B and both slits are opened. The light beam used is of such low intensity that only one photon at a time is emitted by S. In this situation each photon is recorded by either one detector or the other, never by both at once. Half of the photons are observed to pass through slit A, half through slit B in random order. This result is consistent with particle behavior. 

Young s double-slit experiment and the Stem-Gerlaeh experiment, as described in the two previous sections, lead to a physical interpretation of the wave function associated with the motion of a particle. Basic to the concept of the wave function is the postulate that the wave function contains all the... 

Figure 3.1 (a) Schematic diagram (not to scale) of Young s double-slit experiment. The narrow slits acts as wave sources. Slits S and S2 behave as coherent sources that produce an interference pattern on screen C. (b) The fringe pattern formed on screen C could look like this. (Reproduced with permission from R. A. Serway Physics for Scientists and Engineers with Modern Physics, 3rd ed, 1990, Saunders, Figure 37.1.)... 

It is observed in Young s double-slit experiment with electrons by Tonomura and coworkers that single electrons observed as dots on the detector screen are accumulated in time to show interference fringes delocalized over the screen [45]. When... 

There is a direct analogy with the fringe pattern that is seen in a Young s double slit experiment, in which the diffraction pattern from two slits produces periodic fringes whose spacing varies inversely with the separation of the slits. The oscillations can also be interpreted in terms of the distortions of the reflected wavefronts in Fig. 7.2 at the Rayleigh angle (Atalar 1979). 

Sofar the imaging results of Fig. 3.1 were discussed in very classical terms, using the notion of a set of trajectories that take the electron from the atom to the detector. However, this description does not do justice to the fact that atomic photoionization is a quantum mechanical proces. Similar to the interference between light beams that is observed in Young s double slit experiment, we may expect to see the effects of interference if many different quantum paths exist that connect the atom to a particular point on the detector. Indeed this interference was previously observed in photodetachment experiments by Blondel and co-workers, which revealed the interference between two trajectories by means of which a photo-detached electron can be transported between the atom and the detector [33]. The current case of atomic photoionization is more complicated, since classical theory predicts that there are an infinite number of trajectories along which the electron can move from the atom to a particular point on the detector [32,34], Nevertheless, as Fig. 3.2 shows, the interference between trajectories is observable [35] when the resolution of the experiment is improved [36], The number of interference fringes smoothly increases with the photoelectron energy. 

---