How to count all ways to arrange Bosons?

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SUMMARY

The discussion focuses on the correct enumeration of states for identical bosons, emphasizing that calculations applicable to distinguishable particles do not hold for identical bosons. Participants pointed out that a specific case was overlooked in the initial enumeration. The correct approach requires acknowledging the indistinguishable nature of bosons, which significantly alters the counting method.

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  • Understanding of quantum mechanics principles, particularly particle statistics.
  • Familiarity with the concept of indistinguishable particles in physics.
  • Knowledge of combinatorial mathematics as it applies to particle arrangements.
  • Basic grasp of bosonic behavior and its implications in quantum systems.
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  • Study the principles of Bose-Einstein statistics in detail.
  • Learn about the mathematical techniques for counting states of indistinguishable particles.
  • Explore examples of boson arrangements in quantum mechanics.
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Homework Statement
This is very basic question but to be honest I dont understand even though I read Pointon's book. The question said what is all possible ways to arrange Bosons and how much is the total configuration. The energy states/levels are = 1E, 2E, and 3E. The total of boson particles are 2, and all of the states should have degeneracy/g_j = 3 and total Energy E = 4.

Is my answer incorrect? Thank you
Relevant Equations
W = \frac{(n+g-1)!}{n!(g-1)!}
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In your enumeration of states, you are missing one case.

Your calculation on the right is correct only for distinguishable particles. This should not apply to identical bosons.
 
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