# What is Fermi gas: Definition and 34 Discussions

An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.This physical model can be accurately applied to many systems with many fermions. Some key examples are the behaviour of charge carriers in a metal, nucleons in an atomic nucleus, neutrons in a neutron star, and electrons in a white dwarf.

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1. ### I Determining the Number of Points in the n-Space

Electron gas is a collection of non - interacting electrons. If these electrons are confined to certain volume (for example, cube of metal), their behavior can be described by the wavefunction which is a solution to the particle in a box problem in quantum mechanics. Allowed energy states for...
2. ### I Fermi Gas Model: Energetic Degeneration & the Pauli Exclusion Principle

In the fermi gas model, there is assumption that there is a 3D potential well, but there is "energetic degeneration" for each three index "nx, ny, nz". Now the problem is with that image, if there is degeration, for some level En there may be 10 distinctive state with same energy, so there is 20...
3. ### I Trying to get a physical understanding of a Fermi gas

I would like to get a more physical interpretation of conduction electrons (fermi gas) in a metal. I imagine ionized valence electrons close to the ions, with the fermi level (highest energy electrons) of the gas participating in conduction. A point of confusion for me...the first ionization...
4. ### I Fermi gas in relativistic limit

In a statistical mechanics book, I learned about the degenerate pressure of a Fermi gas under the non-relativistic regime. By studying the low-temperature limit (T=0), we got degenerate pressure is ##\propto n^{5/3}## (n is the density). And then I was told that in astrophysical objects, the...
5. ### I Query regarding Fermi Gas model

I was reading an introductory text on nuclear models and came across the Fermi Gas model. I understand that the depth of the potential well of the proton should be less than the depth of the potential well of the neutron due to the Coulombic repulsion between the protons. But I did not...
6. ### I Spin density in an (ideal) Fermi gas

Hi, some time ago our professor told us (en passant) to evaluate this quantity: $$<F|n_m( \mathbf x) n_{m'}(\mathbf x) |F> - <F|n_m( \mathbf x)|F><F|n_{m'}(\mathbf x) |F>$$ And then he said: "you'll find that this quantity may not be zero. In particular when the electron are correlated it will...

I find that $$U=\int Z \epsilon D(\epsilon) e^{-\epsilon β}d\epsilon=\frac{gV}{(2\pi)^3}\int Z \frac{(\hbar)^2k^2}{2m}k^2 (4\pi)e^{-β\frac{(\hbar)^2k^2}{2m}}dk$$ where g=2s+1=2, $$Z=e^{βµ}$$ and $$D(\epsilon)=\frac{gV}{(2\pi)^3}k^2 4\pi$$ for the density of states From here, I can use $$c_v... 8. ### Average speed of molecules in a Fermi gas My first most obvious attempt was to use the relation ##<\epsilon> = \frac{3}{5}\epsilon_F## and the formula for kinetic energy, but this doesn't give the right answer and I'm frankly not sure why that's the case. My other idea was to use the Fermi statistic ##f(\epsilon)## which in this case... 9. ### Question about Fermi energy and heat capacity of a Fermi gas Attempt: 10. ### Thermal Physics: Fermi Gas and chemical potential Hi all, I have an issue trying to understand the following paragraph from Blundell's book. How, exactly, does the definition of ##\mu_0 = E_F## "make sense"? In the sentence after 30.21, it seems to say that the mean energy for a system with ##N## particles differs from that of a system with... 11. ### A Magnetic response of a degenerate Fermi gas I know that in a Fermi gas, the two common responses to a lo field are Pauli par. and Landau dia. and the last becomes the H-VA effect My question is, it is the same treatment in degenerated Fermi Gas? 12. ### A Fermi gas in a magnetic Field? I am currently working in astromagnetism. My question is, somebody knows if a fermi gas (degenerate electrons) can increase or decrease de total magnetic field due to an influence of an external magnetic field and if somebody have information about that. I know that an external magnetic field... 13. ### A Conductivity and Integration over Fermi-Sphere? Hi, I am reading "An Introduction of Solid State Physics" from Ibach Lüth and don't understand the integration process. They write$$\sigma=\frac{e^2}{8\pi^3 \hbar} \int df_{E}dE \frac{v^2_x(\bf{k})}{v(\bf{k})} \tau(\bf{k}) \delta(E-E_F)  = \int_{E=E_F}^{}df_{E}...

Good evening. I'm currently studing dense matter and nuclear matter above 10^8 g/cm^3, and i know well how to insert a beta equilibirum condition in a free Fermi gás at T=0. \sqrt{K^2_{F,n}+m^2_n}=\sqrt{K^2_{F,p}+m^2_p}+\sqrt{K^2_{F,e}+m^2_e} But how do i insert the same condition of...
15. ### Fermi temperature of a 1D electron gas

Homework Statement Consider a one-dimensional metal wire with one free electron per atom and an atomic spacing of ##d##. Calculate the Fermi temperature. Homework Equations Energy of a particle in a box of length ##L##: ##E_n = \frac{\pi^2 \hbar^2}{2 m L^2} n^2## 1D density of states...
16. ### I Fermi gas at the absolute zero T

I'm currently studying Thermodynamic properties of a Fermi gas at the absolute zero temperature. I get how the internal energy, pressure... etc of the gas are derived. For example, in computing the internal energy, one sums up all the energy of states weighted by its average occupation...
17. ### I Differential number of particles in Fermi gas model

I'm practicing for the Physics GRE, and came across a question that has me stumped. "In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...
18. ### Trying to relate nuclear physics to solid state (fermi gas)

In nuclear physics we have talked about the liquid drop model and the fermi gas model. My question is can a Fermi liquid and a Fermi gas be directly described using these models? Are they the same thing? i.e. If I wanted to decribe the difference between a fermi gas and a fermi liquid could I...
19. ### How does the density of states change with temperature?

Homework Statement Part (a): Plot fermi energy as a function of N Part (b): Derive the density of states and find its value Part (c): How many atoms reside at 20% of fermi energy? Estimate diameter of cloud Part (d): For the same atoms without spin, why is the cloud much smaller...
20. ### Are All States in a Free Fermi Gas Equal?

edit* never mind figured it out thanks.
21. ### Regime of Fermi gas or liquid?

Hi, I was wondering if anyone could clarify for me what the correct regime is for treating the electrons in a material as a Fermi gas. When is it that you must use Fermi liquid theory?
22. ### Polarization of a Ideal Fermi Gas

Homework Statement At T=0, what is the largest density that a gas can be completely spin polarized by a magnetic induction of 10 telsas Homework Equations μn= 10^-26 J/T mass= 5*10^-27 kg spin= 1/2 The Attempt at a Solution I am really not sure where to begin. The spin...
23. ### What is the equation for the bulk modulus of a Fermi gas?

Homework Statement It is just a line of equation from my Stat Mech textbook, that says B = -V(dp)/(dV) = (10U)/(9V) = (2nEf)/3 where B is the bulk modulus, V is the volume, p is the pressure, U is the energy, n is the number per unit volume and Ef is the fermi energy. Homework...
24. ### Fermi Gas in Pathria | Magnetic Field & Maxwell Boltzman Statistics

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...
25. ### Kinetic Energy of 3D Fermi Gas at Absolute Zero

Show that the kinectic energy of a three-dimensional fermi gas of N free electrons at absolute zero is (Mathematica code used) u = 3/5 N Subscript[\[Epsilon], F] Now I know total energy of N particles is this integral u = \!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$...
26. ### Degenerate Fermi Gas: Why is it Called Degenerate?

Why is it called degenerate ?? Is it because all levels upto fermi level are filled or all degeneracies of the energy levels that are present occupied at T = 0k . In deriving the average occupation no. for a deg fermi gas , we have used classical idea of momentum that is integrating over a...
27. ### Degenerate Fermi Gas: Exploring the Basics

Why is it called degenerate ?? Is it because all levels upto fermi level are filled or all degeneracies of the energy levels that are present occupied at T = 0k . In deriving the average occupation no. for a deg fermi gas , we have used classical idea of momentum that is integrating over...
28. ### Quantum gases. The ideal Fermi gas

Relations for an ideal Fermi gas: \frac{P}{k_BT}=\frac{1}{\lambda_D^3}f_{5/2}(\lambda) \frac{1}{\upsilon}=\frac{1}{\lambda_D^3}f_{3/2}(\lambda) But in some book books I find \frac{P}{k_BT}=\frac{g}{\lambda_D^3}f_{5/2}(\lambda)...
29. ### Chemical Potential in a Degenerate Fermi Gas

in a Fermi gas, we know that when the temperature is much less than the Fermi energy, it becomes a degenerate gas. does this mean the chemical potential of the system be very large?
30. ### Boundary Conditions for Fermi Gas

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?
31. ### 2D Fermi Gas: Find Density of States

Although I have some major conceptual problems with the Fermi gas as treated in my solid state physics notes (see this thread: https://www.physicsforums.com/showthread.php?t=161222, I have attempted to solve this homework problem in an analogous manner to the solution for the 3D Fermi gas given...
32. ### Exploring Quantum Numbers & Wavefunctions in Fermi Gas

Hi, I have a question about the discussion of the free-electron (Fermi) gas in my solid-state physics notes. In the free electron model, you basically have particles in a box, and the state of any particle is described by four quantum numbers, nx, ny, nz, and ms, the spin magnetic quantum...
33. ### Ground state energy of free electron fermi gas

Can someone explain to me why the ground state energy of a free electron fermi gas is not just: E = 2 \int_0^{k_f} \frac{\hbar^2 k^2}{2m} 3k^2 dk Where the factor of two is due to the fact that there are two electron states for each value of k. The idea is to add up all the energies of...
34. ### Fermi Gas Model / Fermi energy and momentum

Hi, Hope somebody can help - I seem to be missing the obvious and bonking my head on the wall. In Wong and also in Feshbach/deShalit, they calculate the Fermi momentum, Kf using the experimental value of Rho-0 and come up with Kf=1.3 fm-1 So far so good. Where I stumble is in...