Potential Source of Confusion When Adjusting the Zero Point of Energy
Attentive students may notice the following problem here:
Two aspects of the model seem to contradict each other: the infinitely high walls of the potential well and the level of the “bottom”.
Question: The potential well is infinitely deep. Yet the position of the “bottom” plays a major role in adjusting the potential well. Shouldn’t the choice of the zero point of energy be completely arbitrary?
Answer: In this problem, the zero point of energy cannot actually be chosen completely freely. There is, in fact, one particularly distinguished energy: the zero point of energy given by the Coulomb potential (i.e. the energy that 
approaches at infinity). Relative to this zero point, electrons with 
are bound, and those with 
are free.
For the potential well, usually only the distance of the energy levels from the “bottom” is relevant. Here, however, this is not the physically interesting quantity. Instead, what matters is the distance of the energy level under consideration from the zero point of energy of the Coulomb potential (see figure). This is why the value of 
is actually relevant: changing leads to a different model potential (one that approximates the Coulomb potential better or worse).