What is Electron gas: Definition and 40 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.
In the Jellium model, it is customary to evaluate the exchange term of the Hartree-Fock equation for plane waves ##\varphi_{\mathbf{k}_i}## as a correction to the energy of the non-interacting electron gas obtaining $$\hat{U}^{ex} \varphi_{\mathbf{k}_i}=-e^2 \left( \int \dfrac{\mathrm{d}^3k}{2...
As in title:
Plugging in the definition is straight forward, I am too lazy to type, I will just quote the book Fetter 1971:
Up to here everything is very straight forward, in particular, since we are working on free electron gas, ##E=\hbar \omega##
However, I have no idea how to arrive...
I'm reading through Hohenberg's seminal paper titled: "Inhomogeneous Electron Gas" that help lay the foundation for what we know of as Density Functional Theory (DFT) by proving the existence of a universal functional that exactly matches the ground-state energy of a system with a given...
Basically the thread title. For some background, I'm trying to model laser-material interactions, where I'm assuming that the laser is interacting with a free electron gas (copper). To model the interaction, I need to determine the properties of the electron gas, such as the heat capacity...
I had another excercise of the long list of the same topic (solid state physic) where I need a bit of help. All other excercise where about interband transition, dispersion relation, refracting and absorption coefficient, x-rays and so on, and I managed to solve them or I think I will be able...
It is well known that the 2D free electron gas fermi momentum can be expressed as follows,
k_F=\left(2\pi n\right)^{1/2}
where n is the electron surface density.
Assuming this 2D electron system can be considered as 2-D tight-binding square lattice whose eigenergy can be written as...
It is well-known that the electron gas of volume V has an equation of state p=p(V) and thus has a bulk modulus $$B=-V(dp/dV)$$. Suppose the electron gas had no underlying lattice but was confined. Do phonons emit and absorb in such an electron gas at finite temperature?
The reason I ask is...
How can I see, by looking at a band structure if the substance in question can be viewed as a free electron gas (FEG) or not?
What characterizes a FEG in a bandstructure plot?
Thanks in advance!
When do we use the Boltzmann equation for density in a Fermi plasma?
n in [cm-3]
and when do we use the ρ=m/V, ρ in [Kg/m3 ]
(this is not an example, I just added the equations to make my question more understandable)
Is the ideal gas only when we have electron and ions? Is the Boltzmann...
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...
Hi guys! I have a problem with this exercise:
1. Homework Statement
The stars called white dwarfs may have inside them a density in order of 1011 kg m-3. For semplicity, we assume:
these stars are made with non interacting protons and electrons at the same quantity and with uniform density...
Homework Statement
An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by
n^2 = 1 - \frac{\omega_P^2}{\omega^2},
where the plasma frequency
\omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)...
Hello everyone! I encountered a problem about the specific heat of electronic gas and I do not understand a formula... so the problem says that experimentally it has been shown that the specific heat of the conduction electrons at constant volume in metals depends on...
Hello,
I am studying transport in the free electron gas model and I don't understand how to compute the average of the electron density current.
We are given the hamiltonian
## H=\int \psi^\dagger(r,t)(-\frac{\hbar^2\nabla^2}{2m}+e\vec{E}\cdot\vec{r})\psi(r,t)##
where the ##psi## operator is...
Consider a slab infinite in x,y direction but very thin in z direction. As a classical model assume that we displace the electron gas surrounding the static iron cores slightly. With this picture, does the electron gas then consitute a harmonic oscillator?
The electric field from an infinite...
For a free electron gas the procedure for determining the density of states is as follows.
Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2\pi/L3=2\pi/V
And from there we can find the number of states at a...
Before I ask the question, let me explain a little bit about myself. I graduated just over a year ago with a bachelors in Physics, and am now starting my first semester of grad school in Energy Engineering. I have been out of practice, and am facing major struggles getting back into my...
Hi all,
I was deriving the free electron gas for practice in 1, 2, and 3 dimensions, and I started wondering why they have different dependencies on energies and what that means. I got:
1D: ##g(E) = \frac{1}{\pi\hbar} \sqrt{\frac{2m}{E}}##
2D: ##g(E) = \frac{m}{\pi\hbar^2}##
3D: ##g(E) =...
I read from a textbook that there are two boundaries conditions that may be used in order to determine the energies of N electron system in a cube of volume V (and side a).
...
(check out the attached file)
...
As you can see in the attached file, the energies got by using the the two...
According to Pauli principle, it is impossible for two electrons in the electron gas to have the same state. on the other hand, we say that each spatial state can be filled by two electrons with opposite spins.
But my question;
Suppose we have two electrons, one spin down and another spin up...
HI!
Also:
I have 1-d electron gas in tight banding model with included interaction between electrons of same spins V_{\uparrow}=-N_{\uparrow}U where U > 0, \sigma=\pm1 is spin up or down, and pauli interaction with outside field B is included. I have to calculate the total energy of gas at...
Homework Statement
In Drude - Lorentz' FREE ELECTRON GAS MODEL , it has been said " since the conduction electrons move in a uniform electrostatic field of ion cores, their potential energy remains constant and is normally taken as zero, i.e., the existence of ion cores is ignored." I don't...
Hydrogen atoms are in ionised state in the Sun?
So the electrons are in a separate gas state?
If, yes, than what is the main properties of that gas:
temperature, partial pressure, velocity distribution, etc.
Can somebody give me a good reference or answers?
Homework Statement
Imagine non-interacting electrons confined to a two-dimensional plane between atomic layers within a crystal. Discuss the properties of the resulting fermi electron gas.
Homework Equations
None
The Attempt at a Solution
I don't really have any idea how to go...
Homework Statement
In a solid state book I am reading the 3 dimensional electron gas is derived. It says, "An unconfined electron in free space is described by the Schrodinger equation where m is the free-electron mass.
The solutions of the equation, phi(r)=1/(2pi)^3 Exp(ik.r) are plane...
Homework Statement
Show that the adiabatic bulk modulus of a free electron gas can be given by
B= \frac{2nE_{F}}{3}
where
n-number density
E_{F} -Fermi energy
Homework Equations
I started with the adiabatic bulk for an ideal gas
K=\gamma P
where...
Homework Statement
Calculate the total internal energy per electron at zero temperature of a free noninteracting gas of electrons of density n, in the following two cases.
a) First assume that states with both spin directions are populated equally.
b) Now assume that the gas is fully...
The longitudinal dielectric function of a gas of free electrons (+ homogeneous positive background) is often described in the Lindhard- or Random Phase Approximation (RPA).
The dielectric function depends on both frequency omega and wavevector k. However, it is non-analytic at the point...
Hi all,
I am trying to learn Hartree-Fock theory on free electron gas. But I am stumbled on one integration that I cannot seem to figure out. Here is the integral:
\int_{k'<k_{F}}\frac{d\textbf{k}'}{(2\pi)^3}\frac{4\pi e^2}{\left|\textbf{k}-\textbf{k}'\right|^2}
I cannot figure out on...
Hi, I have two questions,
1. I am reading the book 'Solid State Physics', 1976, by Aschcroft and Mermin. I am reading chapter II about 'The Sommerfeld Theory of Metals'. (I hope anyone here have the same book..)
I found it hard to figure out one integral on the equation (2.30) on...
Could anyone tell me the equation of state of an electron gas, or where I could read it from? By equation of state I mean a relation between pressure, density etc etc.
What is the pressure exerted by a Fermi electron gas at 0K? I know that from Pauli's exclusion principle there must be a non zero pressure even at 0K, but what is the quantitative relation between this pressure and the electron concentration? How do I go about to derive this?
Hello!
In my course of solid states physics we use the fermi-dirac statistics for a free electron gas in metals. The fermi wave length of the electrons is about 1 Angström. Now, the wavelength may be intepreted as something as a coherence range - the electron should forget about the state of...
Hi all,
I'm struggling to understand the relationship between electrical conductivity and Bragg reflection in a 2D square lattice free electron gas with lattice spacing a.
Is it the case that Bragg reflection in the electron gas results in electrical resistivity?
My understanding of...
i was thinking this for few days
suppose glouds of neutral particles ne (m=0,5Mev) exists in galaxys halo. ne would easily decay
to electron or positron near atoms nucleus or if its disturbed some way. (so it wouldn't be found
in high energy lab) - ne could be produced only by direct pair...
I try to to some first principle calculation in the environment of free electron gas. For intance, the total energy of one atom or a cluster in the free electron gas.
What kind of calculation program could I choose ? I only know that VASP provide an opion to create charged background...