How to Develop a Theoretical Model
One could in principle go ahead and derive physical properties from first principles by solving the Schrödinger equation for the composite solid. Practically, this is neither possible nor useful. The number of particles involved is way too high even for the most powerful computers and besides that one usually does not know the positions of all particles involved.
Thus, a different approach is required. In such situations it is always a good idea to make some simplifications that reduce the complexity significantly while still being valid for most relevant cases. Therefore we will initially use the following simplifications:
- The solid consists only of a small number of different constituents
- The constituents are rather simple e.g. single atoms or only small molecules
- The materials exhibit a high level of large scale ordering ( $\rightarrow$ crystalline material)
- Possible defects/impurities in the solid are neglected
Fortunately, many relevant solids fulfil these constraints.