When this occurs, the apparent horizontal motion of the wave ceases and the wave appears to 'stand' in the same place in the rope. If the person adjusts the rhythm of their hand just right, they can arrange for the crests and troughs of the wave moving toward the tree to exactly coincide with the crests and troughs of the reflected wave. This causes interference to occur between the wave traveling toward the tree and the reflected wave traveling back toward the person. When a wave travels down a rope and encounters an immoveable boundary (like a tree), the wave reflects off the boundary and travels back up the rope.

In an earlier part of this text, a wave was described in which a rope was tied to a tree and a person jerked the other end of the rope up and down to create a wave in the rope. Scientists call these waves standing waves.ДЇigure 6.4: Some fans getting ready for 'the wave' as it passes through the stadium. There are, however, special waves that stay in one spot. Again, this is an example of a traveling wave, because it moves from fans at one end of the stadium to fansДЄt the other. Similarly, if you're in the stands watching the Oakland As play ball, you might find yourself jumping up and cheering as 'the wave' passes through the stadium (Figure 6.4). This, of course, implies that ocean waves are traveling waves because they actually move through the water.

When you finally do, you know that even though the big wave may be quite a distance off, it will eventually arrive at your surfboard and carry you in to shore. When you're sitting on your surfboard, trying to catch a good wave, you'll often look out to sea in the hopes of spotting a 'big one' (Figure 6.3). Most of the waves that you're probably familiar with are known as traveling waves, because they travel or move.

Define an electron wave function and electron density and relate these terms to the probability of finding an electron at any point in space.ДЄn Electron is Described as a Standing Wave.

Explain why electrons form standing waves, and what this means in terms of their energies.

Distinguish between traveling and standing waves.

We'll talk more about these special matter waves in the next section.

As a result, they are forever trapped in the matter that holds them. Unlike puddle waves, which eventually die out as they escape from the puddle, matter waves never do, because matter waves don't move. But as soon as you leave the puddle alone, the surface of the puddle will become as calm as glass.

As long as you disturb the puddle with your stick, the puddle will have waves in it. When you do, what you'll notice is that the waves you create actually move from your stick out to the edge of the puddle, where they disappear. You can form waves in a puddle by stirring the puddle with a stick. If you think carefully, you'll realize that this isn't true of most other waves with which you are familiar. Unlike ocean waves or puddle waves, matter waves are 'trapped' in space and, as a result, can never die out, escape, or disappear. It might be tempting to visualize matter waves as being just like ocean waves, or waves in a puddle, but it turns out that matter waves are special. In the last lesson, you learned that electrons and, in fact, all objects with mass, have wavelike properties. 3 Each Wave Function has an Allowed Energy Value.2 An Electron is Described as a Standing Wave.

Schrodinger wave function