- #1
phyzmatix
- 313
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First of all, I just want to check if my understanding of degeneracy is correct:
The degeneracy of an excited state is the number of combinations of quantum numbers that will result in the same energy level.
?
Secondly, if this is right and if we have an equation
[tex]E_{xy}=\frac{\hbar^2 \pi^2}{2ma^2}(n_x^2+n_y^2)[/tex]
from which we wish to obtain the four lowest possible energy levels and their corresponding degeneracies, then is it correct to do that as follows
[tex]E_{11}=\frac{\hbar^2 \pi^2}{2ma^2}(1^2+1^2)=2\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{12}=\frac{\hbar^2 \pi^2}{2ma^2}(1^2+2^2)=5\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{21}=\frac{\hbar^2 \pi^2}{2ma^2}(2^2+1^2)=5\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{22}=\frac{\hbar^2 \pi^2}{2ma^2}(2^2+2^2)=8\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
With corresponding degeneracies
[tex]E_{11} = 1[/tex]
[tex]E_{12}=E_{21}=2[/tex]
[tex]E_{22}=1[/tex]
I'm not sure if there's an equation that could be useful to calculate the degeneracy perhaps?
Thanks in advance!
phyz
The degeneracy of an excited state is the number of combinations of quantum numbers that will result in the same energy level.
?
Secondly, if this is right and if we have an equation
[tex]E_{xy}=\frac{\hbar^2 \pi^2}{2ma^2}(n_x^2+n_y^2)[/tex]
from which we wish to obtain the four lowest possible energy levels and their corresponding degeneracies, then is it correct to do that as follows
[tex]E_{11}=\frac{\hbar^2 \pi^2}{2ma^2}(1^2+1^2)=2\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{12}=\frac{\hbar^2 \pi^2}{2ma^2}(1^2+2^2)=5\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{21}=\frac{\hbar^2 \pi^2}{2ma^2}(2^2+1^2)=5\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
[tex]E_{22}=\frac{\hbar^2 \pi^2}{2ma^2}(2^2+2^2)=8\frac{\hbar^2 \pi^2}{2ma^2}[/tex]
With corresponding degeneracies
[tex]E_{11} = 1[/tex]
[tex]E_{12}=E_{21}=2[/tex]
[tex]E_{22}=1[/tex]
I'm not sure if there's an equation that could be useful to calculate the degeneracy perhaps?
Thanks in advance!
phyz