Solving Degeneracy Equation: General Formula & More

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SUMMARY

The discussion centers on the concept of degeneracy in quantum mechanics, specifically in the context of homework for a second quantum mechanics class. The user seeks a general formula for calculating degeneracy, referencing the sum of the squares of quantum numbers, [n_x]^2 + [n_y]^2 + [n_z]^2, to determine the degeneracy value (d). It is concluded that there is no universal formula applicable to all quantum systems; instead, one must solve the time-independent Schrödinger's equation to identify the eigenfunctions and their corresponding degeneracies.

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Students of quantum mechanics, particularly those tackling concepts of degeneracy and eigenfunctions, as well as educators seeking to clarify these topics in their curriculum.

steveb
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Hello all.
I'm presently on my first set of homework for my 2nd QM class, and am stuck on the degeneracy issue.
I thought that I had a more comprehensive explanation of it in my notes from the first semester, but was not able to find them.
I know that I'm suppposed to take the sum of the squares of the choices---
[n_x]^2 + [n_y]^2 + [n_z]^2 will give me the total values of the n's, and that should then tell me my d value.
For the first 3 energy states-- n=1, 2, 3, d=1 for n=1, d=3 for n=2&3.
What is the general formula for degeneracy? One that would give me the total qty of choices?
Thanks.
Pardon me if I sound out of it. I had nasal surgery on friday, and am still not feeling all there.
 
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steveb said:
What is the general formula for degeneracy? One that would give me the total qty of choices?
There is no general formula for an arbitrary quantum system. You have to set up and solve the (time-independent) Schrödinger's equation, see what eigenfunctions you come up with.
 

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