Advantages and disadvantages of the box-potential approximation

Advantages and disadvantages of the method:

Although the model is fairly crude, it provides:

The quantization of the energy levels in the hydrogen atom as a consequence of the spatial confinement (here caused by the “walls” of the potential well).
The correct dependence of the energy values on the principal quantum number $n$ : $E \sim - \dfrac{1}{n^2}$ (why actually?)
Agreement of the numerical values to the right order of magnitude.

Methodologically, one advantage of this approach can be seen in the fact that the procedure (namely replacing the actual potential by a different one) is an example of an approximation method commonly used in physics

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