Degeneracy of the Quantum Linear Oscillator

  • Thread starter mavanhel
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So, today while doing my homework for statistical mechanics I was reading about the quantum linear oscillator in the textbook, "Classical and Statistical Thermodynamics" by Ashley H. Carter. In it, after discussing the quantized energy it says:

"Note that the energies are equally spaced and that the ground state has a 'zero-point' energy equal to [tex]\frac{hv}{2}[/tex]. The states are nondegenerate in that [tex]g_{j} = 1[/tex] for all [tex]j[/tex]."

The book gives no further clarification on this point as, but I was wondering why the degeneracy for this problem is one for all states.

This problem occurs at the beginning of chapter 15, "The Heat Capacity of a Diatomic Gas" and makes the following considerations:
  • consider an assemply of N one-dimensional harmonic oscillators.
  • The oscillators are loosely coupled (ie. small energy exchange between them).
  • The oscillators are free to vibrate in one dimension freely.

This does not tell us anything about the degeneracy, so why is this system nondegenerate?
 

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DrClaude
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The vibration of a diatomic is modelled as a one-dimensional harmonic oscillator, for which there is a single eigenfunction for each eigenenergy. There is nothing more to it.
 

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