The difference

[Robbe Daelman]

The difference lies in the equations used to mathematically describe the problem: The equations of classical mechanics can be solved exactly in a reasonable amount of time, so the engineer building the bridge can perform these calculations beforehand and be sure that the bridge will not collapse. The Schrödinger equation on the other hand, can in most cases only be solved approximately which leaves room for error. Furthermore, deviations in the initial conditions have very different effects in these two regimes. If the bridge becomes slightly longer for example, the engineer will have to add more support structures but the resulting bridge won’t be that different from the original. If however one slightly changes the spacing of nuclei in a solid for example, the energy eigenvalues of the whole system will change which can lead to vastly different behavior in the solid.

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