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# Section 1.1: Static Images Versus Physlet Animations

A Physlet is a Physics (Java) Applet written at Davidson College. We use Physlets to animate physical phenomena and to ask questions regarding the phenomena. Sometimes you will need to collect data from the Physlet animation and perform calculations in order to answer the questions presented. Sometimes simply viewing the animation will be enough for you to complete the exercise.

The Physlet animations presented in Physlet Quantum Physics 2E will be similar to the static images in a textbook. There are differences that need to be examined, however, because we will be making extensive use of these types of animations throughout Physlet Quantum Physics 2E. First consider the following image.1

Images of the time evolution of the position-space probability density corresponding to a quantum-mechanical wave packet at times near its collision with an infinitely hard wall.

This image represents the time evolution of the position-space probability density corresponding to a quantum-mechanical wave packet as it approaches, collides with, and reflects from an infinitely hard wall. The packet has an initial momentum to the right and the images are shown at equal time intervals. We are supposed to imagine the motion of the packet by reading the images from left to right. We notice that as the packet moves to the right its leading edge encounters the infinite wall first and is reflected back towards the middle of the well. There are several interesting features about this problem that are not depicted in the image however. While we get the general sense of what happens, we lose a lot of the specific information. This is especially apparent at the times when the packet is in contact with the wall.2

Now consider the Physlet animation of the same situation. Restart. Press the "Play" button to begin the animation. Note that the VCR-type buttons beneath the animation control the animation much like buttons on a VCR, CD, or DVD player. Specifically,

• Play starts the animation and continues it until either the animation is over or is stopped.
• Pause pauses the animation. Press play to resume the animation.
• Step » steps the animation forward in time by one time step.
• « Step steps the animation backward in time by one time step (the size of the time step varies with the animation). In this animation there is no "« Step" button.
• Reset resets the animation time to the initial time. Then, press "{lay" to run the animation from the beginning.

Make sure you understand what these buttons do, since you will need to use them throughout the rest of the book when you interact with the Physlets on ComPADRE.

In addition to these buttons, there are hyperlinks on the page that control which animation is played. For example, on this page, Restart reinitializes the applet to the way it was when the page was loaded. On other pages there will often be a choice of which animation to play, but Restart always restores the animation to its initial condition.

So why animation in addition to static images? Most of the examples typically studied in quantum physics are often limited to a few simple exactly solvable problems. Interactive animations allow for the study of a wide variety of different situations, many not solvable analytically. In addition, the time evolution and dynamics of quantum-mechanical systems are often difficult to understand if you are trying to describe it with a static picture (or even a series of static pictures). Because the examples in this book are interactive animations, you can actually see the details of the quantum-mechanical time development and change the initial conditions to explore other scenarios.

Restart (or reset) the animation and play it again. Watch the collision with the right wall in detail. What do you notice about the motion of the packet? First, notice that the packet spreads with time. This is a quantum-mechanical effect (see Chapter 8 for details). Also note that the collision with the wall is rich in detail that may be missed if you only have one image of the collision.

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1One of the first such computer-generated images was discussed by A. Goldberg, H. M. Schey, and J. L. Schwartz, "Computer-generated Motion Pictures of One-dimensional Quantum-mechanical Transmission and Reflection Phenomena," Am. J. Phys. 35, 177-186 (1967).
2Such a collision is often called a quantum bounce. See, for example, M. Andrews, "Wave Packets Bouncing Off of Walls," Am. J. Phys. 66 252-254 (1998) and M. Doncheski and R. Robinett, "Anatomy of a Quantum 'Bounce,'" Eur. J. Phys. 20, 29-37 (1999), and M. Belloni, M. A. Doncheski, and R. W. Robinett, "Exact Results for `Bouncing' Gaussian Wave Packets," to appear in Phys. Scr. 71, 136-140 (2005).

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