Question

Sketch the n=1 and n=7 wave functions for the potential energy shown in FIGURE EX40.15

Short answer

The sketch

Step-by-step solution

Step 1. Given information

For $n=1$, we have only one antinode, and most of the region is the classically forbidden region. So, before the node in the classically forbidden region, the wave function increases exponentially. After the node, the wave function decreases exponentially, as shown in the figure.

For$n=7$, there are 7 nodes and 6 antinodes. There are classically forbidden regions before and after the nodes. The wavelength is large initially and then decreases and from the center of the well. The wavelength again increases the same way for amplitude.

Step 2. The sketch