Section 1.5: Getting Data Out
Please wait for the animation to completely load.
In Section 1.2 you learned about units and how to click-drag in an animation to get data from the animation. Here we will discuss several other ways in which data are depicted in animations. Restart.
Press the "play" button to begin. Shown in the animation (ħ = 2m = 1) is the probability density corresponding to an accelerating Gaussian wave packet. When you press the "play" button, the packet will move across the screen in a predefined way (obeying the rules of quantum mechanics). Along with the probability density are depictions of the packet's average position: as an on-screen numerical statement, as data in a table, and as a function of time on a graph. You may of course click-drag in the animation to measure average position (since a Gaussian is symmetric about its maximum value) and amplitude as well.
Why do we show all of these different representations? Because they provide complementary ways of thinking about the phenomena. Click Restart and play the animation again. Notice how the different representations of the motion change with the motion of the packet. With a lot of practice, physicists can look at the motion of an object and can tell you the various properties of the motion. How do we do that? By having different mental representations in our heads. Specifically,
- on-screen numerical statements of position facilitate the measurement process, as the value is always given. These statements can be for any variable, not just position.
- data tables are used to compare two or more values that are changing like in the animation where <x>, <p>, and t are changing.
- graphs are used to summarize all of the data corresponding to the motion of an object that occurs during a time interval. The graph summarizes all of the data shown in the on-screen calculation and the data table. When you get a good-looking graph, you can usually right-click on it to clone the graph and resize it for a better view. Try it!
In practice, we will never set up an animation to give you all of these depictions simultaneously. We usually pick one or two representations that best represent the phenomena.
Note that some animations depict motion that started before the animation begins and continues beyond the time that the animation ends. In the animations on this page, the packet starts at rest at t = 0 but continues its motion beyond the t = 5 mark when the animation ends.