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Why can't electrons move inside the valence band? Is that the Pauli exclusion principle - and is it true that the electrons cant move even when the valence band is only partially filled?
Why can't electrons move inside the valence band? Is that the Pauli exclusion principle
- and is it true that the electrons cant move even when the valence band is only partially filled?
Okay I thought it might be the Pauli exlusion principle. So each band has only a finite number of energy and when all these are filled the electrons cannot move unless the next band is close.
But I must admit that there is one thing I really don't understand about all this. We are using the eigenstates to determine which states an electron can occupy. But this is quantum mechanics! Superposition of eigenstates are possible state to leading to almost infinite combinations of possible states. Why are these not relevant for solid state theory? I think I am misunderstanding something completely.
How does this symmetry arise? Why most the electrons move so as to cancel out any net current?Looking at it from another angle, electrons in the valence band can always move. However, electrons near the top of the valence band move in the opposite direction to electrons near the bottom of the valence band, so that in a full band no net current arises.
The problem is not that I don't know how to distinguish between them. The problem is the whole statistical approach where it only seems that the eigenstates are relevant for the statistics when in reality there exists an infinite amount of superpositions of eigenstates for the many particle Hamiltonian, which the many-particle system could be in. https://www.physicsforums.com/showthread.php?t=715106You have to distinguish between eigenstates of a one particle hamiltonian and eigenstates of a many particle hamiltonian. If you consider but a single electron, all these superpositions of Bloch states are relevant. However in solid state theory, we are interested in systems containing many electrons.
There we use the Bloch one electron states only to build up a convenient basis for the many particle hamiltonian, e.g. via antisymmetrized Slater determinants.
How does this symmetry arise? Why most the electrons move so as to cancel out any net current?