Question

Summarize the similarities are differences between the three simple bound cases considered in this chapter.

Short answer

Similarly: All of the cases had a non-zero ground state Kinetic Energy and the form standing waves.

Differences: In case of infinite square well, the wave function doesn’t extend in to area outside walls, but in other cases it did.

Step-by-step solution

Step-1:Difference in the Energies

The three simple bond cases considered were the infinite well, the harmonics oscillators and the finite square well. All of those have a non-zero ground-state Kinetic Energy from standing waves. The harmonics oscillators and the infinite well can take on infinite number of states while the finite square well has a finite limit to the number of states it can hold.

Step-2:Difference in the Wave Functions

In the case of the infinite square well, the wave functions doesn’t extend into the area outside of the walls, but In the other two cases the wave function can extend into the classically forbidden area.

For the finite square well, the energy level becomes more spaced as more are added while the harmonic oscillators are evenly spaced.

Hence, the point of differences & similarities b/w three simple bound cases considered in this chapter are discussed above.