Partition Functions for FermiDirac and BoseEinstein particles

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SUMMARY

The partition functions for two indistinguishable particles in three quantum states at temperature T are derived for both Fermi-Dirac and Bose-Einstein statistics. The Fermi-Dirac partition function is given by Z = exp[-beta * e] + exp[-2 * beta * e] + exp[-4 * beta * e], while the Bose-Einstein partition function is Z = 1 + exp[-beta * e] + 2*exp[-3 * beta * e] + exp[-4 * beta * e] + exp[-6 * beta * e]. These expressions account for the indistinguishability of the particles and the specific energy levels they occupy.

PREREQUISITES
  • Understanding of Fermi-Dirac statistics
  • Understanding of Bose-Einstein statistics
  • Knowledge of quantum states and energy levels
  • Familiarity with the concept of partition functions in statistical mechanics
NEXT STEPS
  • Study the derivation of partition functions in statistical mechanics
  • Explore the implications of indistinguishability in quantum statistics
  • Learn about the applications of Fermi-Dirac and Bose-Einstein statistics in physical systems
  • Investigate how temperature affects the behavior of quantum particles
USEFUL FOR

Students and researchers in physics, particularly those focusing on statistical mechanics, quantum mechanics, and thermodynamics. This discussion is beneficial for anyone studying the behavior of indistinguishable particles under different statistical frameworks.

mark.laidlaw19
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Homework Statement


Consider two particles, each can be in one of three quantum states, 0, e and 3e, and are at temperature T. Find the partition function if they obey Fermi Dirac and Bose Einstein statistics.

Homework Equations

The Attempt at a Solution


I have obtained solutions to both :

FD, Z = exp[-beta * e] + exp[-2 * beta * e] + exp[-4 * beta * e]

BE,Z = 1 + exp[-beta * e] + 2*exp[-3 * beta * e] + exp[-4 * beta * e] + exp[-6 * beta * e]

I have figured these out by thinking through the possible states for the particles. I'm assuming they have to be indistinguishable. I just want to confirm that my thinking has led to the correct results.

Many thanks
 
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What expression for Z did you not provide under 2. Homework Equations ?
 

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