When a weak periodic potential is applied to a material, it can cause energy band gaps to form, which can have a significant influence on the electron states of the material. Specifically, the electron states that are most influenced by a weak periodic potential are those that are close to the energy band gaps or boundaries.
In a solid material, electrons are typically found in energy bands, which are ranges of allowed energies. Energy band gaps occur when there are ranges of energies that are not allowed, meaning that electrons cannot exist in those energy states. When a periodic potential is applied to a material, it can cause energy band gaps to form in regions of the energy spectrum that were previously continuous.
Electron states that are close to these energy band gaps or boundaries are most influenced by the periodic potential because they are more sensitive to changes in the local energy landscape. For example, if a periodic potential is applied that creates a small energy gap near a particular energy level, the electrons with energies closest to that level will be affected the most. This is because small changes in the energy landscape can cause electrons to shift from one energy band to another, or to be scattered in different directions.
In summary, the electron states that are most influenced by a weak periodic potential are those that are close to the energy band gaps or boundaries. These states are more sensitive to changes in the local energy landscape and can be affected by even small changes in the periodic potential.
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