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Quantum Stat­ist­ics is the tool required in order to work with a whole host of phys­ic­al phe­nom­ena. For this reas­on, I’ve ded­ic­ated this sec­tion to the applic­a­tions of the quantum the­ory to top­ics such as Black­body Radi­ation and sol­id state physics.

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Video # Video Tutori­al Title Remarks
1 Max­well Boltzmann Aver­age Speed Cal­cu­late the aver­age speed of particles in a gas (say)
2 Max­well Boltzmann Vrms Cal­cu­late the root mean squared velo­city of a gas (say)
3 Deriv­a­tion of the Fermi Level 1/2 Free elec­tron the­ory IOT derive a func­tion for the Fermi Level
4 Deriv­a­tion of the Fermi Energy 2/2 A sim­il­ar video to # 33 a but much quick­er and with less back­ground theory
5 Dens­ity of States Writ­ten as a Func­tion of E-Fermi Using the res­ult from video # 33 b
6 Total Elec­tron Con­tri­bu­tion to a Solid’s Energy  
7 Aver­age Energy Via Par­ti­tion Function A net trick! Use it to derive all the occu­pancy func­tions in a flash!
8 Power Series Res­ult­ing from 1/(1-x)  Anoth­er neat trick for using the Par­ti­tion Func­tion to derive the B.E. Occupancy
9 Aver­age Energy of a Quantum Har­mon­ic Oscillator Ein­stein mod­elled solids as LHOs to dis­cov­er quant­ised phonons
10 Heat Capa­city of Har­mon­ic Oscil­lat­or System Einstein’s LHO approach to solids dis­covered that they obeyed B.E. statistics
11 Ein­stein For­mula for the Spe­cif­ic Heat Capacity A sim­il­ar video to # 36 b : Ein­stein, his phon­ons and Bose Ein­stein statistics
12 Par­ti­tion Func­tion and Free Energy Why is the Par­ti­tion Func­tion to useful?
13 The Gibbs Factor An improve­ment upon the Boltzmann Factor to account con­ser­va­tion of particles
14 The Planck Dis­tri­bu­tion 1/2 Black­body Radi­ation and the Ultra­vi­olet Catastrophe
15 Photon Elec­tro­mag­net­ic Energy Density Energy dens­ity in the Planck Dis­tri­bu­tion (light as photon quanta)
16 Black­body Radi­ation : Con­tinu­ous Energy Levels The Ultra­vi­olet Cata­strophe occurred when con­tinu­ous energy levels were assumed
17 The Planck Dis­tri­bu­tion 2/2 Planck’s for­mula for Black­body Radi­ation via quant­isa­tion of energy
18 Wien’s Dis­place­ment Law Deriv­a­tion
19 Stefan Boltzmann Law  I=σT4
20 The Sol­id Angle or Steradian Vital for flux calculations
21 Photon Flux Cal­cu­la­tion of irradiance
22 Som­mer­feld Expan­sion 1/3 The neces­sary Taylor Series expansion
23 Som­mer­feld Expan­sion 2/3 A full deriv­a­tion of Sommerfeld’s expansion
24 Som­mer­feld Expan­sion 3/3 The con­tri­bu­tion of elec­trons to a solid’s energy
25 Laser Co-effi­cients Ein­stein LASER absorp­tion and emis­sion co-efficients
26 Laser Gain Co-efficient Deriv­a­tion
27 Elec­tron Orbitals Intro­duc­tion to the Peri­od­ic Table
28 Helm­holtz The­or­em 1/2 Deriv­a­tion of scal­ar potential
29 Helm­holtz The­or­em 2/2 Deriv­a­tion of vec­tor potential

 

quantum stat­ist­ics kahn academy phys­ics applic­a­tions fermi level photon black­body radi­ation laser elec­tron orbit orbit­al som­mer­feld expan­sion wien’s dis­place­ment law flux quantum stat­ist­ics kahn academy phys­ics applic­a­tions fermi level photon black­body radi­ation laser elec­tron orbit orbit­al som­mer­feld expan­sion wien’s dis­place­ment law flux quantum stat­ist­ics kahn academy phys­ics applic­a­tions fermi level photon black­body radi­ation laser elec­tron orbit orbit­al som­mer­feld expan­sion wien’s dis­place­ment law flux 

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