![]() ![]() Let us explore what happens if we try to follow a particle. ![]() ![]() It is somewhat disquieting to think that you cannot predict exactly where an individual particle will go, or even follow it to its destination. Those who developed quantum mechanics devised equations that predicted the probability distribution in various circumstances. There is a certain probability of finding the particle at a given location, and the overall pattern is called a probability distribution. After compiling enough data, you get a distribution related to the particle’s wavelength and diffraction pattern. However, each particle goes to a definite place (as illustrated in Figure 1). The idea quickly emerged that, because of its wave character, a particle’s trajectory and destination cannot be precisely predicted for each particle individually. Both patterns are probability distributions in the sense that they are built up by individual particles traversing the apparatus, the paths of which are not individually predictable.Īfter de Broglie proposed the wave nature of matter, many physicists, including Schrödinger and Heisenberg, explored the consequences. Double-slit interference for electrons (a) and protons (b) is identical for equal wavelengths and equal slit separations. The overall distribution shown at the bottom can be predicted as the diffraction of waves having the de Broglie wavelength of the electrons.įigure 2. Each electron arrives at a definite location, which cannot be precisely predicted. The building up of the diffraction pattern of electrons scattered from a crystal surface. Repeated measurements will display a statistical distribution of locations that appears wavelike. But if you set up exactly the same situation and measure it again, you will find the electron in a different location, often far outside any experimental uncertainty in your measurement. Experiments show that you will find the electron at some definite location, unlike a wave. What is the position of a particle, such as an electron? Is it at the center of the wave? The answer lies in how you measure the position of an electron. Matter and photons are waves, implying they are spread out over some distance. ![]() Explain the implications of Heisenberg’s uncertainty principle for measurements.Use both versions of Heisenberg’s uncertainty principle in calculations.If you're focusing on trying to watch the speed, then you may be off a bit when measuring the exact time across the finish line, and vice versa. The physical nature of the system imposes a definite limit upon how precise this can all be. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |