Degeneracy of the Quantum Linear Oscillator

  • Thread starter mavanhel
  • Start date
2
0
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?
 

DrClaude

Mentor
6,969
3,141
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.
 

Want to reply to this thread?

"Degeneracy of the Quantum Linear Oscillator" You must log in or register to reply here.

Related Threads for: Degeneracy of the Quantum Linear Oscillator

Replies
12
Views
33K
  • Posted
2
Replies
29
Views
29K
Replies
4
Views
1K
  • Posted
Replies
2
Views
14K
Replies
1
Views
2K
Replies
5
Views
4K
Replies
6
Views
1K
Replies
1
Views
516

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top