How Do Quantum Statistics Affect Energy Level Degeneracies in a SHO?

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SUMMARY

This discussion focuses on the degeneracies of energy levels for two indistinguishable spin-0 particles in a simple harmonic oscillator (SHO) framework. The identified degeneracies are as follows: (0,0) has 1, (1,0) and (0,1) combined have 1, (2,0) and (0,2) along with (1,1) yield 2, and combinations like (1,2) and (2,1) also yield 2, following the pattern 1,1,2,2,3,3,4,4. When considering two fermions of the same type with the same magnetic eigenvalue, the degeneracies shift to 0, 1, 1, 2, 2, 3, 3. The results presented are consistent with quantum statistical principles.

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  • Understanding of quantum mechanics, specifically the principles of indistinguishable particles.
  • Familiarity with simple harmonic oscillator (SHO) models in quantum physics.
  • Knowledge of quantum statistics, including Fermi-Dirac and Bose-Einstein statistics.
  • Basic grasp of energy level degeneracies and their implications in quantum systems.
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Kontilera
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Lets say we have two spin 0 particles that don't interact more than being indistingishable..
what are the degenercies for the energylevels?
I would say:

PHP:
(n1, n2)                                  D
---------------------------------------

(0,0)                                     1
((1,0)+(0,1))                             1

((2,0)+(0,2)); (1,1)                      2 
((1,2) + (2,1));((3,0)+(0,3))             2
with the pattern begin 1,1,2,2,3,3,4,4...
If we insted study 2 fermions of same type and same m-eigenvalue. I then got 0, 1, 1, 2, 2, 3 ,3...
Do you agree with my results?
 
Last edited:
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Looks fine to me.
 

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