Solving Degeneracy Equation: General Formula & More

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In summary, the conversation discusses the concept of degeneracy in quantum mechanics and the difficulty in finding a general formula for it. The formula for calculating degeneracy is taking the sum of the squares of the choices, [n_x]^2 + [n_y]^2 + [n_z]^2. However, there is no general formula and it is necessary to solve the Schrödinger's equation to determine the eigenfunctions and their corresponding degeneracy. The speaker also mentions having had nasal surgery and apologizes if they sound out of it.
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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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  • #2
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.
 

Related to Solving Degeneracy Equation: General Formula & More

1. What is degeneracy in terms of scientific equations?

Degeneracy in scientific equations refers to the phenomenon where multiple solutions exist for a given set of conditions. This can occur when there are multiple variables or parameters that can affect the outcome of the equation, resulting in multiple possible solutions.

2. How is degeneracy typically represented in equations?

Degeneracy in equations is often represented by a degeneracy factor or degeneracy coefficient, which is a numerical value that indicates the number of solutions for a given set of conditions. This factor is typically denoted by the symbol "g" and is often used in statistical mechanics and quantum mechanics.

3. What is the general formula for solving degeneracy equations?

The general formula for solving degeneracy equations is g = n!, where g is the degeneracy factor and n is the number of distinct states or solutions. This formula assumes that all states are equally likely to occur and that there are no restrictions or constraints on the solutions.

4. Are there any other methods for solving degeneracy equations?

Yes, there are other methods for solving degeneracy equations, such as the use of combinatorics and probability theory. These methods take into account the specific conditions and restrictions of the problem and can provide more accurate solutions in certain cases.

5. How can degeneracy equations be applied in real-world scenarios?

Degeneracy equations have many applications in various fields of science, including physics, chemistry, and biology. They can be used to predict the behavior of complex systems, understand the properties of materials, and analyze data in statistical studies. They are also essential in the development of technologies such as quantum computing and molecular modeling.

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