Boundary Conditions for Fermi Gas

[plxmny]

Hi

I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?

 

[Epicurus]

Periodic boundary conditions allow you to calculate properties for infinite systems which is more appropriate than just making a large box. This is the basis for the band theory of solids.

 

[charng]

Hi there, as a scientist, I can understand your confusion about the use of periodic boundary conditions for a fermi gas in a cube. Let me try to explain the reasoning behind it.

Firstly, it is important to understand that fermi gas is a theoretical model used to describe the behavior of electrons in a solid. It assumes that the electrons are free to move within the solid and are not affected by any external potential. Therefore, in this model, the electrons are not confined to a particular region or well potential.

Now, coming to the use of periodic boundary conditions, it is a mathematical technique used to simplify the calculations in a system with periodic symmetry. In the case of a fermi gas in a cube, the periodicity arises from the fact that the cube has equal sides and the electrons can move freely in all directions. By using periodic boundary conditions, we can simulate the behavior of an infinite system, which is more realistic for a solid state system.

On the other hand, using a finite well potential would limit the movement of the electrons and would not accurately represent the behavior of a solid. Additionally, the work function, which is related to the energy required to remove an electron from a solid, is a concept that is applicable to real-world systems and not to the idealized model of a fermi gas.

I hope this explanation helps you understand the use of periodic boundary conditions in the context of a fermi gas in a cube. If you have any further questions, please feel free to ask.