Fermi Gas in Pathria | Magnetic Field & Maxwell Boltzman Statistics

In summary, the electron's binding status and the choice of statistical distribution can impact the magnetization of the grand partition function in different ways.
  • #1
shadi_s10
89
0
Hi again!
another question!

I statistical mechnics by Pathria, it has all about the fermi gas in a magnetic field in chapter8

I have another question
what if the electron was in some boundaries?
what would change then about magnetization of grand partition function?
For example for an electron in an atom which is BOUND TO THE NUCLEUS
or what if we have used maxwell boltzman statistics instead of fermi dirac for and electron gas?
what would happen the?


please help!
I'm sooooooooooo confused! :confused:
 
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  • #2
If the electron is bound to the nucleus, then it will not be affected by the magnetic field and the magnetization of the grand partition function will remain unchanged. However, if we use Maxwell-Boltzmann statistics instead of Fermi-Dirac for an electron gas, then the magnetization of the grand partition function will be different due to the different statistical distributions. Specifically, the magnetization will be lower in the case of Maxwell-Boltzmann statistics than in the Fermi-Dirac case.
 

FAQ: Fermi Gas in Pathria | Magnetic Field & Maxwell Boltzman Statistics

What is a Fermi gas?

A Fermi gas is a collection of particles, such as electrons, that obey the laws of quantum mechanics and are confined in a container. These particles interact with each other and their surroundings, but are not bound by any potential energy barriers.

How does a magnetic field affect a Fermi gas?

A magnetic field can cause the energy levels of a Fermi gas to split, resulting in different energy states for particles with different spin orientations. This can lead to changes in the behavior and properties of the gas, such as its electrical conductivity.

What is the Maxwell-Boltzmann distribution in relation to a Fermi gas?

The Maxwell-Boltzmann distribution is a statistical distribution that describes the distribution of energies among particles in a gas at a given temperature. In a Fermi gas, this distribution can be used to understand the behavior of particles with non-quantized energy levels at high temperatures.

How is the energy of a Fermi gas related to its temperature?

The energy of a Fermi gas is directly proportional to its temperature. As the temperature increases, the particles in the gas have more energy and can occupy higher energy states. This relationship is described by the Maxwell-Boltzmann distribution.

What are some real-world applications of studying Fermi gases in magnetic fields?

Studying Fermi gases in magnetic fields has important implications in fields such as condensed matter physics, materials science, and quantum computing. It can also help us understand the behavior of electrons in metals, which is essential for developing new electronic devices and technologies.

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