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.
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...
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...
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...
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...
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...
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
$$c_v...
My first most obvious attempt was to use the relation ##<\epsilon> = \frac{3}{5}\epsilon_F## and the formula for kinetic energy, but this doesn't give the right answer and I'm frankly not sure why that's the case. My other idea was to use the Fermi statistic ##f(\epsilon)## which in this case...
Hi all, I have an issue trying to understand the following paragraph from Blundell's book.
How, exactly, does the definition of ##\mu_0 = E_F## "make sense"? In the sentence after 30.21, it seems to say that the mean energy for a system with ##N## particles differs from that of a system with...
I know that in a Fermi gas, the two common responses to a lo field are Pauli par. and Landau dia. and the last becomes the H-VA effect
My question is, it is the same treatment in degenerated Fermi Gas?
I am currently working in astromagnetism. My question is, somebody knows if a fermi gas (degenerate electrons) can increase or decrease de total magnetic field due to an influence of an external magnetic field and if somebody have information about that.
I know that an external magnetic field...
Hi,
I am reading "An Introduction of Solid State Physics" from Ibach Lüth and don't understand the integration process.
They write $$\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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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]\), \(0\)...
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...
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...
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)...
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?
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?
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...
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...
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...
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...