Physics in a nutshell

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Simplifying Assumptions

How to Develop a Theoretical Model

One could in principle go ahead and derive physical properties from first principles by solving the SchrÃ¶dinger 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.

Simplifications

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.

References

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