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The Max­well Boltzmann dis­tri­bu­tion (or occu­pancy func­tion) describes the stat­ist­ic­al nature of Clas­sic­al Particles (such as air molecules). The videos presen­ted in this video tutori­al series are taken from the lar­ger set of videos on Quantum Stat­ist­ics. The mul­ti­pli­city func­tion is util­ised IOT derive the occu­pancy func­tion. There­after, the aver­age speed and Vrms are derived.

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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 Max­well Boltzmann Mul­ti­pli­city Function A deriv­a­tion which is used later to derive the occu­pancy function
7 Dens­ity of States, Num­ber Dens­ity and Occupancy Intro­du­cing fun­da­ment­al quant­it­ies of quantum statistics
8 The Boltzmann Factor A deriv­a­tion of a most import­ant quantity
9 The Par­ti­tion Function A deriv­a­tion of yet anoth­er import­ant and use­ful quantity
10 Dens­ity of States 1/7 Sch­rodinger Equa­tion for particle in infin­ite poten­tial well
11 Dens­ity of States 2/7 Vec­tor ‘k’ space and Vec­tor ‘n’ space
12 Dens­ity of States 3/7  Scal­ar ‘k’ and scal­ar ‘n’ space
13 Dens­ity of States 4/7  Dens­ity of states in momentum space
14 Dens­ity of States 5/7  Dens­ity of space in velo­city space
15 Dens­ity of States 6/7  Dens­ity of states in energy space
16 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
17 Max­im­ising the Occu­pancy Function How to cal­cu­late the most prob­able distribution
18 Meth­od of Lag­range Multipliers Learn why the Meth­od of Lag­range Mul­ti­pli­ers Works
19 Max­well Boltzmann Dis­tri­bu­tion / Occu­pancy Function Deriv­a­tion of the occu­pancy func­tion for clas­sic­al particles
20 Eval­u­ation of α and the Ther­mo­dy­nam­ic β Max­im­ising the occu­pancy func­tion res­ults in α and β: I eval­u­ate them here
21 Max­well Boltzmann Scal­ar Speed Distribution Deriv­a­tion of scal­ar speed dis­tri­bu­tion for clas­sic­al particles such as air molecules
22 Max­well Boltzmann Aver­age Speed Cal­cu­late the aver­age speed of particles in a gas (say)
23 Max­well Boltzmann Vrms Cal­cu­late the root mean squared velo­city of a gas (say)

 

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