Degree of Freedom: Explaining n,l & m Quantum Numbers

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SUMMARY

The discussion centers on the quantum numbers n, l, and m, which define the degrees of freedom for an electron in a hydrogen atom. These quantum numbers arise from solving the hydrogen Schrödinger equation and specify the energy levels and angular momentum direction of the electron. The term "degrees of freedom" refers to the number of independent parameters that define the system's state, aligning with the roles of n, l, and m in quantum mechanics.

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An electron moves around a nucleus in 3d space so it is required that there should be 3 quantum no. each specifying its degree of freedom .

the three quantum no. are n,l & m , but n,l& m specify the energy levels avalaible to electron & m specifies the direction of angular momentum vector .

So what is actually meant by degree of freedom & how do n,l & m specify it ?
 
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i'm not sure what you are asking, do you want a claasical explenation of what n,l and m mean?

n,l and m simply come from solving the hydrogen Schödinger equation. And from wikipedia

Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. In mathematical terms, the degrees of freedom are the dimensions of a phase space.

so this definition agrees with what n,l and m does, i guess.
 
I studied my self and found the ans from hydrogen atom
 

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