Nice derivations of Maxwell, Fermi-Dirac and Bose-Einstein distributions

In summary, Maxwell, Fermi-Dirac, and Bose-Einstein distributions are statistical probability distributions named after the scientists who first derived them. They play a crucial role in understanding the behavior of particles in various physical systems and were derived using classical and quantum mechanics. These distributions are only applicable to certain types of particles and have practical applications in physics, chemistry, and engineering.
  • #1
DaTario
1,029
35
Hi all,

Does anybody know some reference (even internet one) that explains in detail the derivation of Maxwell´s velocity and/or energy distribution on an ensemble of atoms/molecules ?
References to Fermi-Dirac distributions and Bose-Eisntein´s are also welcome.

Best Regards,

DaTario

Comment: My experience with Huang´s Statistical Mechanics was very bad.
 
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  • #2
Tolman's Principles of Statistical Mechanics is a good source. I didn't care much for Huang either.
 
  • #3
I suggest Greiner's book on thermodynamics & statistical mechanics. It's pretty clear and there's no shortcut in any calculations.

Daniel.
 
  • #4
Thank you a lot Dextercioby and Tide.
 

1. What are Maxwell, Fermi-Dirac, and Bose-Einstein distributions?

Maxwell, Fermi-Dirac, and Bose-Einstein distributions are statistical probability distributions that describe the behavior of particles in a system. They are named after the scientists who first derived them: James Clerk Maxwell, Enrico Fermi and Satyendra Nath Bose, and Albert Einstein, respectively.

2. What is the significance of these distributions in physics?

These distributions play a crucial role in understanding the behavior of particles in various physical systems, including gases, semiconductors, and superconductors. They help us understand phenomena such as phase transitions, heat capacity, and electron behavior.

3. How were these distributions derived?

Maxwell's distribution was derived by considering the velocities of molecules in a gas and applying the principles of classical mechanics. Fermi-Dirac and Bose-Einstein distributions were derived using quantum mechanics, specifically the principles of indistinguishability and the Pauli exclusion principle.

4. Are these distributions only applicable to certain types of particles?

Yes, Maxwell's distribution is applicable to classical particles with mass, while Fermi-Dirac and Bose-Einstein distributions are applicable to quantum particles such as electrons, protons, and photons.

5. What are the practical applications of these distributions?

These distributions have a wide range of applications in physics, chemistry, and engineering. They are used to understand and predict the behavior of particles in various systems, as well as in the development of technologies such as semiconductors, lasers, and superconductors.

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