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 The Fermi Dirac distribution (or occupancy function) describes the statistical nature of Fermions (particles with an rational spin such as electrons, the up-quark and helium-3). The videos presented in this video tutorial series are taken from the larger set of videos on Quantum Statistics. The multiplicity function, the Density of States, the Partition Function etc., are all utilised IOT derive the occupancy function in three separate ways.

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Video #

Video Tutorial Title

Remarks

1

Macro and Micro States

Unless you understand these you’re going to struggle at a later stage

2

The Multiplicity Function

The number of ways of arranging the particles

3

Distinguishable VS Indistinguishable Particles

Classical particles, Bosons and Fermions!

4

Classical Particles, Bosons & Fermions

Defining each type of particle

5

Fermi Dirac Multiplicity Function

A derivation which is used later to derive the occupancy function

6

The Boltzmann Factor

A derivation of a most important quantity

7

The Partition Function

A derivation of yet another important and useful quantity

8

Average Energy Via Boltzmann Factor

An extremely useful trick IOT greatly simplify statistical calculations

9

Density of States 1/7

Schrodinger Equation for particle in infinite potential well

10

Density of States 2/7

Vector ‘k’ space and Vector ‘n’ space

11

Density of States 3/7 

Scalar ‘k’ and scalar ‘n’ space

12

Density of States 4/7 

Density of states in momentum space

13

Density of States 5/7 

Density of space in velocity space

14

Density of States 6/7 

Density of states in energy space

15

Why the # ‘Dots’ in n Space = The Volume in n Space

Why you can alculate the number of n space states by calculating the volume

16

Maximising the Occupancy Function

How to calculate the most probable distribution

17

Method of Lagrange Multipliers

Learn why the Method of Lagrange Multipliers Works

18

Evaluation of α and the Thermodynamic β

Maximising the occupancy function results in α and β: I evaluate them here

19

Fermi Dirac Distribution Function 1/3

Derivation of the occupancy function for Fermions

20

Derivation of the Fermi Level 1/2

Free electron theory IOT derive a function for the Fermi Level

21

Derivation of the Fermi Energy 2/2

A similar video to Q.S. # 33 a but much quicker and with less background theory

22

Density of States Written as a Function of E-Fermi

Using the result from Quantum Statistics video # 33 b

23

Total Electron Contribution to a Solid’s Energy

 

24

Fermi Dirac Distribution Function 2/3

Derivation using the Gibbs Factor rather than multiplicities

25

Fermi Dirac Distribution Function 3/3

Derivation using the Grand Partition Function

 

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