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For one dimensional crystal, when we have periodic boundary condition, we may think that the atoms are arranged in a circle, and so each lattice point will be equal to other lattice point and the translation symmetry is conserved. And for three dimensional crystal, due to periodic boundary condition, each atom will feel the same in the lattice. They are in ...


I have figured out the answer. Since the velocity depends on $\nabla_kE(k)$, it does not matter where the parabola is centered.


The Fermi velocity is related to the Fermi energy $\epsilon_F=\frac12m_{\text e}v_F^2$. Actually, the Fermi energy $\epsilon_F$ is the chemical potential of the electron gas (that is the minimum energy required to add an extra electron to the gas). The energies of the electrons are distributed, according to the Fermi-Dirac distribution, as $$ ...


How does a molecule form? At the most general level the idea is that there exist lower energy states with the atoms in the molecule closer to each other, and the original joint state of the atoms had a nonzero ability to transition into that lower energy state and give up some energy. The rest is really some thermodynamics. If everything is hot and dense ...


The Pauli Exclusion Principle means that not every electron can be at the very lowest energy level.

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