Ground and Excited States in a Potential Well (QM)

[Poop-Loops]

Here's the problem:

http://www.phys.washington.edu/users/karch/324/2007/hw3.pdf

Just the first one.

Okay, so my understanding is that the first state of Psi (ground state) is just an arc, like a Gaussian distribution, starting from 0 at E0 and finishing at 5a also at the level of E0.

The next ones are just sine waves at higher frequencies.

So would I just draw a high frequency sine wave of amplitude E0 until I get to the "jump" at 2a, and then just decrease the the amplitude that that point, but keep the frequency the same?

Or since the frequency corresponds to energy, and I don't have as much of a jump from E0 to the bottom of the well, I should keep the amplitude constant the whole time, but decrease the frequency once I get to the "jump" at 2a?

The book only mentions an infinite square well and doesn't really go into it.

 

[Poop-Loops]

Sorry, but I still haven't figured this one out.

Is the energy level 0 meaningless here, since a particle can't get below the ground state (E0) in energy?

So it would be a high-frequency sine wave with the amplitude being from E to E0? I still don't see the significance of the potential jump in the middle.