# Viability of particle in a box modeling

1. Nov 19, 2014

### 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?

2. Nov 19, 2014

### 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.

3. Nov 19, 2014

### 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.

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