# Fermi-Dirac distribution

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• chikchok
In summary, the Fermi-Dirac distribution is a probability distribution developed by Enrico Fermi and Paul Dirac in the 1920s to describe the distribution of particles in a quantum system at thermal equilibrium. It is used to determine the probability of a particle occupying a particular energy state and takes into account the Pauli exclusion principle. The Fermi energy, which is the highest energy state a particle can occupy at absolute zero temperature, is significant in understanding the behavior of electrons in solids. This distribution differs from the Maxwell-Boltzmann distribution in that it is applicable to particles with half-integer spin and is used in various fields of science, including solid state physics, quantum mechanics, and statistical mechanics.

#### chikchok

TL;DR Summary
Fermi-Dirac distribution
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)

##f(\epsilon)## goes to zero as ##\epsilon \rightarrow \infty## for a finite temperature (##T>0##).

At absolute zero, ##T=0##, then ##f(\epsilon > \epsilon_\mathrm{F}) = 0##, where ##\epsilon_\mathrm{F}## is the Fermi energy.

chikchok

## What is the Fermi-Dirac distribution?

The Fermi-Dirac distribution is a statistical distribution that describes the probability of a particle occupying a specific energy state in a system of many identical particles that obey the Pauli exclusion principle.

## What is the significance of the Fermi-Dirac distribution?

The Fermi-Dirac distribution is important in understanding the behavior of fermions, which are particles with half-integer spin, such as electrons, in a system. It helps to explain phenomena such as electron degeneracy pressure in dense materials and the conductivity of metals.

## What is the difference between the Fermi-Dirac distribution and the Bose-Einstein distribution?

The Fermi-Dirac distribution describes the behavior of fermions, while the Bose-Einstein distribution describes the behavior of bosons, which are particles with integer spin. This difference is due to the Pauli exclusion principle, which states that fermions cannot occupy the same quantum state, while bosons can.

## What is the Fermi energy in the Fermi-Dirac distribution?

The Fermi energy is the highest energy state occupied by fermions at absolute zero temperature in a system described by the Fermi-Dirac distribution. It is a measure of the energy required to add or remove a fermion from the system.

## How is the Fermi-Dirac distribution related to the Fermi-Dirac statistics?

The Fermi-Dirac distribution is a mathematical expression that describes the probability of a particle occupying a specific energy state in a system, while the Fermi-Dirac statistics is a set of rules that govern the behavior of fermions in a system. The Fermi-Dirac distribution is derived from the Fermi-Dirac statistics.