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ian2012
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How can an electron's momentum be less than the Fermi momentum? Since the Fermi momentum (energy) is measured at absolute zero.
At absolute zero the fermi momentum is the highest momentum an electron can have in the system. Most electrons sit below this energy. As you increase the temperature you are able to thermally excite electrons close to the fermi surface to energies above Pf and Ef. The probablity of this exciatation is given by the fermi-dirac distribution.ian2012 said:How can an electron's momentum be less than the Fermi momentum? Since the Fermi momentum (energy) is measured at absolute zero.
Who said they didn't move? A bound state does not mean that you glued the electron to the side of an ion. The point is that most electrons sit deep within the fermi sea and therefore it is nearly impossible for them to be excited to even the lowest unoccupied state. Thus they do not contribute to heat capacity, etc.ian2012 said:How would electrons have momentum (move) within occupied states? What would it look like intuitively?
Yes, the story goes something like this.ian2012 said:it is QM isn't it.
The Fermi momentum is a measure of the maximum momentum that an electron can possess in a solid. It is closely related to the electron momentum, which is the product of its mass and velocity. In general, the Fermi momentum is significantly larger than the electron momentum due to the high velocities of electrons in solids.
The Fermi momentum and Fermi energy are closely related, as they both depend on the electron density in a solid. The Fermi energy is the highest possible energy that an electron can possess at absolute zero temperature, and it is directly proportional to the Fermi momentum. In fact, the Fermi momentum can be calculated from the Fermi energy using the relation pF = √(2mEF), where m is the electron mass.
The Fermi momentum plays a crucial role in understanding the electronic properties of solids. It determines the behavior of electrons in a material, such as their energy levels and conductivity. It also influences many physical phenomena, such as the thermal and electrical conductivity, and the magnetic properties of a solid.
The Fermi momentum is an intrinsic property of a solid and cannot be directly changed or controlled. However, it can be indirectly influenced by changing the electronic density or the Fermi energy through external factors, such as temperature, pressure, or doping with impurities.
The Fermi momentum determines the shape and properties of the energy bands in a solid. The energy bands represent the allowed energy levels for electrons in a material, and the Fermi momentum determines the maximum energy level that can be occupied by electrons at absolute zero temperature. This, in turn, affects the electronic behavior and properties of a material, such as its electrical and thermal conductivity, and its magnetic properties.