# What is Fermi dirac: Definition and 16 Discussions

Fermi-Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926 (although Fermi derived it before Dirac). Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.
Fermi–Dirac (F–D) statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the F–D distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. F–D statistics is most commonly applied to electrons, a type of fermion with spin 1/2.
A counterpart to F–D statistics is Bose–Einstein (B–E) statistics, which applies to identical and indistinguishable particles with integer spin (0, 1, 2, etc.) called bosons. In classical physics, Maxwell–Boltzmann (M–B) statistics is used to describe particles that are identical and treated as distinguishable. For both B–E and M–B statistics, more than one particle can occupy the same state, unlike F–D statistics.

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1. ### A Thermal Properties of the Free Electron Gas: Fermi-Dirac Distribution

Hello I have some doubts about the relationship between the probability of occupying an electronic state defined by the Fermi Dirac distribution and the relationship to the number N of free electrons in a solid of N atoms. In particular I refer to the Section 2.2 of Solid State Physics...
2. ### I Is the Fermi-Dirac distribution equal to zero at the state of highest energy?

I`m sorry if this seems too obvious, just trying to clarify something. When Fermi-Dirac distribution is equal to zero , can we assume it is the state of the highest energy? (Because the propability of occupation is zero)
3. ### Fermi-Dirac distribution at T->0 and \mu->\epsilon_0

The limit itself is pretty easy to calculate ##lim_{T->0} \ lim_{\mu->\epsilon_F} \ (e^{\frac{(\epsilon_F - \mu)}{kT}}+1)^{-1} = \frac{1}{2}## But I'm very confused about changing ##\epsilon_\vec{k}## to ##\epsilon_F##. Why do we do this?
4. ### I Another question from Ashcroft and Mermin: Fermi-Dirac Distribution

Good Day : i reached the page 40 of Ashcroft Mermin book and after the equation 2.38 there is this expression of E(a,N) which is equal to Helmoltez Free energy F = U - TS , how this two terms F , E are related ? anyone can provide adequate explanation , and few useful references Best...
5. ### Is Fermi-Dirac Probability Part B Solvable?

Hi dear friends Please reffer to my work , I did part ( a ) Can someone help me to solve part( b ) Please
6. ### Calculating Fermi Dirac Probability - Part B Guide

Hi dear friends Please reffer to my work , I did part ( a ) only Could you please help me to do part ( b ) I don't know how to do it.
7. ### A Normalization constant of Fermi Dirac distribution function

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you
8. ### Arithmetic mean Fermi Dirac & Bose Einstein

Hi everybody, I was doing one asignment form class, I was tasked to prove that in one system, the arimetic mean of FD and BE distributions is equal to MB's distribution for undishtingable particles. After doing the numbers I found out that it actually was, but I don't know why this happens, can...
9. ### The application of of Fermi Dirac statistics in the white dwarf

hi guys, I wonder if I have fully understood the Fermi Dirac statistics properly, but I have a question on it regarding its application in the white dwarf research. I read the Fermi energy is applicable for T=0, now if the core of a white dwarf is too hot then how can we apply the Fermi Dirac...
10. ### Entropy of a Fermi dirac ideal gas

Hello Homework Statement From the expression of the partition function of a fermi dirac ideal gas ln(Z)=αN + ∑ ln(1+exp(-α-βEr)) show that S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>) Homework Equations S=k( lnZ+β<E>) <nr>=-1/β ∂ln(Z)/∂Er <E>=-∂ln(Z)/∂β The Attempt at a Solution I...
11. ### Pions vs. Fermi Dirac Statistics and Bose-Einstein Statistics

Hello! I have a small question, and I am not sure if I am missing something: Today I glanced at the wikipedia page for Pions, and saw this: Statistics: Bosonic Can anyone explain to me why a quark paired with a anti-quark obey Bose-Einstein Statistics? If quarks obey Fermi-Dirac statistics...
12. ### Fermi dirac distribution at T->0

Studying the free electron model I found the fermi dirac distribution and the book told me that when T->0 we have that the fermi energy is equal to the chemical potential... why?
13. ### Fermi Dirac distribution function

I have a question that is puzzling me as always...The Fermi-Dirac distribution function is (at T=0): f\epsilon=\frac{1}{e^{\beta(\epsilon-\epsilon_{F})}+1} and we know that we can subsitute f\epsilon by 1 for \epsilon< \epsilon_{F} and 0 otherwise. However what is f(-\epsilon)? The answer is...
14. ### When were Bose-Einstein and Fermi-Dirac statistics first defined?

Hi everyone I need the historical articles that bose and fermi integrals were defined for the first time. Can anyone help me?
15. ### Fermi Dirac- missing something from Ashcroft derivation

[SOLVED] Fermi Dirac- missing something from Ashcroft derivation Homework Statement Deriving Fermi Dirac function following ashcroft all good up to equation 2.43 but then it does the folowing at 2.44 and I can't see how you reach 2.44. Homework Equations as (2.43) f_{i}^{N}= 1-...
16. ### Fermi Dirac (FD) and Maxwell Boltzmann (MB)

I have a homework problem that asks me to interpret the two curves for when the Fermi level (Ef) is 0.25 eV. I ploted the two graphs and both of them look nothing alike when E < Ef. But both plots predict a probability of essentially zero when E > Ef. I was wondering why is there such a large...