Viability of particle in a box modeling

[center o bass]

I've noticed that the example of a particle in a box is heavily used even for physical situations where there is no obvious box: for example when finding the degeneracy pressure in a neutron star one calculates the fermi-energy from a 3D-particle in a box.

So I wondered: is there any good reason why the particle in a box-model holds for a large variety of situations?

Does this has to do with the pauli-exclusion principle? I.e. that the position is constrained by $\delta x \delta_p = \hbar /2$ and we can think of these boxes as $\delta x$ wide?

 

[VantagePoint72]

The "box" in the particle-in-a-box calculation is not necessarily a literal one with solid barriers. The "box" is the shape of the potential energy curve that confines the particle. It's a reasonable approximation for any potential that is small over some finite range before sharply increasing.

 

[dextercioby]

The particle in a (rigid wall) box is a perfect theoretical example for the mathematical subleties of quantum mechanics, usually swept under the carpet when textbooks are written and students are taught.