Absolutely Small - Michael D. Fayer [26]
BACK TO THE PHOTOELECTRIC EFFECT
In Chapter 4, the photoelectric effect was described in terms of photons, which are particles that behave in some sense like bullets of light. One photon strikes one electron and knocks it out of a piece of metal (see Figure 4.3). The description of the photoelectric effect showed that the classical description of light as an electromagnetic wave was incorrect. A new concept had to be introduced to explain both the photoelectric effect and the fact that photons could produce an interference pattern. The Born interpretation of the wavefunction as a probability amplitude wave gave the photon the necessary wavelike characteristics, so that photons could produce an interference pattern. However, in discussing the probability amplitude waves in connection with the interferometer, we only considered the location of the photon in terms of two rather large regions of space; a photon was in a superposition state, T1 + T2, with equal probabilities of being in leg 1 and leg 2 of the interferometer. The photoelectric effect implied that a photon is quite small. Chapter 6 will show how a superposition of probability amplitude waves can produce a photon that is very small in size. The ideas will lead to one of the central and most nonclassical aspects of quantum mechanics, the Heisenberg Uncertainty Principle.
6
How Big Is a Photon and the Heisenberg Uncertainty Principle
IN CHAPTER 5, WE LEARNED that a photon in an interferometer interferes with itself. In some sense, a photon can be in more than one place at a time. The photon location is described as a probability amplitude wave. This is not like a water wave, a sound wave, or even a classical electromagnetic wave. The wave associated with a photon (or other particles like electrons) describes the probability of finding the particle in some region of space. In the interferometer problem (Figures 3.4 and 5.1), a single photon was in leg 1 and leg 2 simultaneously, with equal probability of finding the photon in either of these regions of space. To understand and describe the location of a photon in more detail, it is necessary to discuss more aspects of waves. We need to know about the nature of the probability amplitude waves, particularly how they combine and what happens when a measurement is made.
The simplest problem to discuss is a free particle, which was introduced in Chapter 2. A free particle could be a photon, an electron, or a baseball. It is a free particle if no forces are acting on it. That is, there is no gravity, no electric or magnetic fields, no photons hitting an electron, no baseball bats hitting the baseball, no air resistance, and so on. With no forces acting on a particle, it has a perfectly defined and unchanging momentum. Thus, if it is moving in a particular direction, it will just keep going in that direction. We can call that direction anything we want, so let’s call it the x direction. Think of a graph with the horizontal axis x. We will just pick the direction of the x axis to be along the direction the particle is moving. In connection with Figure 2.5, we talked about a classical particle moving along x with a classical momentum p. Here we want to discuss the nature of a quantum particle with momentum p.
PARTICLES HAVE WAVELENGTHS