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5

A quick google search leads one immediately to the wikipedia page on this particular theorem. The first paragraph of this page states: The Bohr–van Leeuwen theorem is a theorem in the field of statistical mechanics. The theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the ...


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Let us decompose the formula to better understand what it means: $\hbar \mathbf k/m$ is the velocity of the electrons $\epsilon_k - \mu$ is the energy relative to the temperature, so if particles with higher energy than the temperature move in a direction, they produce a positive thermal energy flux, particles with lower energy an negative flux. ...


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You'll want a much bigger heatsink!! (and maybe just one TEC) If it's being cooled only by convection then maybe a heat sink area* that is 10 times that of the TEC. (maybe bigger) The classic mistake with a TEC is to make the heat sink too small. With too small a heatsink the hot side of the TEC gets hotter, more thermal leakage through the TEC, it has ...


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If efficiency is the issue, then definitely parallel TECs (or use a single unit rated for twice the power, same thing). The only reason for stacking TECs is to get a lower temperature. However that comes at great expense to efficiency and overall power consumption. Another point is that paralleling TECs is actually more efficient overall. The reason is ...


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Well, we are not only looking at the electrons of an object when we look at it. What I understood your basic question to be is why we see different objects having different color. Well the reason for that is because different materials are able to reflect only certain frequencies of light. The reason for this is a little more complex. Color in itself is ...


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The colors depend on the frequency of light. Let me explain. In atoms, there are various discrete energy levels that electrons can occupy. A photon that has energy (which remember depends of its frequency) which matches exactly the difference between the electron and the next excited state, will get absorbed by that electron and get excited to the next ...


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Let's assume, you take a one-dimensional chain of atoms and compress it. In order to investigate the bandstructure, you will need to determine the electronic wavefunctions of quantum-mechanically allowed states. If you know your wavefunctions for the initial condition, before you compress your chain of atoms, you need to also scale the solution in order to ...


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A quasi-crystal has no long-range translational symmetry, but it does have long range orientational symmetry. The lattice sites all occur at well defined angles, and in well-defined planes. It is reflection from these planes that causes the well-defined spots. The fact that there is no translational symmetry within those planes does not bear on the ...


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According to my limited understanding of density functional theory. Coulomb interaction is one of the correlation effects. Besides Coulomb interaction, there are interaction due to Pauli exclusion principle and change of kinetic energy compared with that of non-interacting electron gas.


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When solving for the spectrum, you assume the solid has infinite extent, and so the electron is not really bound. Thus you can get a continuum of momentum. Consider for example the trivial case where there are no atoms, and you just have a free electron in space. Then the energy is proportional to momentum squared, and momentum can be arbitrarily big, so ...


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Ok, I am by no means and expert on solid state but I might be a little helpful. Band structure in solids arises due only to periodicity of the lattice. It all comes down to this periodicity. Periodicity of the lattice makes the potential also periodic. This periodicity has many (interesting) consequences (Bloch states and bla bla bla) but the one that ...



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