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The Bose Ein­stein dis­tri­bu­tion (or occu­pancy func­tion) describes the stat­ist­ic­al nature of Bosons (particles with an integer spin such as photons, mesons, and heli­um-4). 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 two 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 Mul­ti­pli­city Rule Summary A sum­mary of the first five mul­ti­pli­city rules
6 Mul­ti­pli­city Rule 6 All particles are indis­tin­guish­able and non-interacting
7 Dens­ity of States, Num­ber Dens­ity and Occupancy Intro­du­cing fun­da­ment­al quant­it­ies of quantum statistics
8 Bose Ein­stein Mul­ti­pli­city Function A deriv­a­tion which is used later to derive the occu­pancy function
9 The Boltzmann Factor A deriv­a­tion of a most import­ant quantity
10 The Par­ti­tion Function A deriv­a­tion of yet anoth­er import­ant and use­ful quantity
11 Dens­ity of States 1/7 Sch­rodinger Equa­tion for particle in infin­ite poten­tial well
12 Dens­ity of States 2/7 Vec­tor ‘k’ space and Vec­tor ‘n’ space
13 Dens­ity of States 3/7  Scal­ar ‘k’ and scal­ar ‘n’ space
14 Dens­ity of States 4/7  Dens­ity of states in momentum space
15 Dens­ity of States 5/7  Dens­ity of space in velo­city space
16 Dens­ity of States 6/7  Dens­ity of states in energy space
17 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
18 Max­im­ising the Occu­pancy Function How to cal­cu­late the most prob­able distribution
19 Meth­od of Lag­range Multipliers Learn why the Meth­od of Lag­range Mul­ti­pli­ers Works
20 Eval­u­ation of α and the Ther­mo­dy­nam­ic β Max­im­ising the occu­pancy func­tion res­ults in α and β: I eval­u­ate them here
21 Bose Ein­stein Dis­tri­bu­tion Func­tion 1/2 Deriv­a­tion of the occu­pancy func­tion for Bosons & dis­cuss­ing the num­ber dens­ity & occupancy
22 Aver­age Energy Via Par­ti­tion Function A net trick! Use it to derive all the occu­pancy func­tions in a flash!
23 Power Series Res­ult­ing from 1/(1-x)  Anoth­er neat trick for using the Par­ti­tion Func­tion to derive the B.E. Occupancy
24 Aver­age Energy of a Quantum Har­mon­ic Oscillator Ein­stein mod­elled solids as LHOs to dis­cov­er quant­ised phonons
25 Heat Capa­city of Har­mon­ic Oscil­lat­or System Einstein’s LHO approach to solids dis­covered that they obeyed B.E. statistics
26 Ein­stein For­mula for the Spe­cif­ic Heat Capacity A sim­il­ar video to # 36 b : Ein­stein, his phon­ons and Bose Ein­stein statistics
28 Par­ti­tion Func­tion and Free Energy Why is the Par­ti­tion Func­tion to useful?
29 The Gibbs Factor An improve­ment upon the Boltzmann Factor to account con­ser­va­tion of particles
30 Bose Ein­stein Dis­tri­bu­tion Func­tion 2/2 Deriv­a­tion using the Gibbs Factor rather than multiplicities

 

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