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Black­body Radi­ation was one of the first top­ics to which quantum stat­ist­ics was applied. In fact, the suc­cess­ful res­ults of Max Planck and oth­ers went a long way to solid­i­fy­ing the status of a the­ory which was not gen­er­ally accep­ted at the time.

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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 Dens­ity of States, Num­ber Dens­ity and Occupancy Intro­du­cing fun­da­ment­al quant­it­ies of quantum statistics
6 Bose Ein­stein Mul­ti­pli­city Function A deriv­a­tion which is used later to derive the occu­pancy function
7 The Boltzmann Factor A deriv­a­tion of a most import­ant quantity
8 The Par­ti­tion Function A deriv­a­tion of yet anoth­er import­ant and use­ful quantity
9 Aver­age Energy Via Boltzmann Factor An extremely use­ful trick IOT greatly sim­pli­fy stat­ist­ic­al calculations
10 Max­well Boltzmann Dis­tri­bu­tion / Occu­pancy Function Deriv­a­tion of the occu­pancy func­tion for clas­sic­al particles
11 Eval­u­ation of α and the Ther­mo­dy­nam­ic β Max­im­ising the occu­pancy func­tion res­ults in α and β: I eval­u­ate them here
12 Bose Ein­stein Dis­tri­bu­tion Func­tion 1/2 Deriv­a­tion of the occu­pancy func­tion for Bosons
13 Dens­ity of States Writ­ten as a Func­tion of E-Fermi Using the res­ult from video # 33 b
14 Aver­age Energy Via Par­ti­tion Function A net trick! Use it to derive all the occu­pancy func­tions in a flash!
15 Power Series Res­ult­ing from 1/(1-x)  Anoth­er neat trick for using the Par­ti­tion Func­tion to derive the B.E. Occupancy
16 Aver­age Energy of a Quantum Har­mon­ic Oscillator Ein­stein mod­elled solids as LHOs to dis­cov­er quant­ised phonons
17 Heat Capa­city of Har­mon­ic Oscil­lat­or System Einstein’s LHO approach to solids dis­covered that they obeyed B.E. statistics
18 Ein­stein For­mula for the Spe­cif­ic Heat Capacity A sim­il­ar video to # 36 b : Ein­stein, his phon­ons and Bose Ein­stein statistics
19 Par­ti­tion Func­tion and Free Energy Why is the Par­ti­tion Func­tion to useful?
20 The Gibbs Factor An improve­ment upon the Boltzmann Factor to account con­ser­va­tion of particles
21 Bose Ein­stein Dis­tri­bu­tion Func­tion 2/2 Deriv­a­tion using the Gibbs Factor rather than multiplicities
22 Dens­ity of States 7/7 Where no peri­od­ic bound­ary con­di­tions exist (pre­vi­ous 6 videos used peri­od­ic BCs)
23 Spher­ic­al Polar Co-ordinates Trans­form from Cartesian to Spher­ic­al Polar co-ordinates
24 The Planck Dis­tri­bu­tion 1/2 Black­body Radi­ation and the Ultra­vi­olet Catastrophe
25 Photon Elec­tro­mag­net­ic Energy Density Energy dens­ity in the Planck Dis­tri­bu­tion (light as photon quanta)
26 Black­body Radi­ation : Con­tinu­ous Energy Levels The Ultra­vi­olet Cata­strophe occurred when con­tinu­ous energy levels were assumed
27 The Planck Dis­tri­bu­tion 2/2 Planck’s for­mula for Black­body Radi­ation via quant­isa­tion of energy
28 Wien’s Dis­place­ment Law Deriv­a­tion
29 Stefan Boltzmann Law  I=σT4
30 The Sol­id Angle or Steradian Vital for flux calculations
31 Photon Flux Cal­cu­la­tion of irradiance

 

 quantum stat­ist­ics kahn academy phys­ics planck dis­tri­bu­tion photon flux bose ein­stein  quantum stat­ist­ics kahn academy phys­ics planck dis­tri­bu­tion photon flux bose ein­stein  quantum stat­ist­ics kahn academy phys­ics planck dis­tri­bu­tion photon flux bose einstein 

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