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it is only zeo at the state of rest .

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In the case of a free electron, there is no external force acting on the electron, so no work is done to displace it. Since potential energy is associated with work done in displacing an object against a force, the potential energy of a free electron is considered to be zero.

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Q: Why the potential energy is zero in free electron case?
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What is the difference between free electron theory and nearly free electron theory?

The free electron theory assumes that electrons in a solid are completely free to move throughout the material, without any interaction with the crystal lattice. In contrast, the nearly free electron theory recognizes that there are some interactions between the electrons and the crystal lattice, leading to energy bands and band gaps in the electron's motion within the solid.


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