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pondzo

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So in class we went through the process of solving the S.W.E for the hydrogen atom.

During the process a constant ##\lambda_n=\frac{ze^2}{4\pi\epsilon_0\hbar}(\frac{\mu}{2|E_n|})^{\frac{1}{2}}## is introduced, where mu represents the reduced mass of the electron.

Later this constant is put on the following restriction so that the power series has a finite power; ##\lambda_n=l+k+1## (where k is the index number for the power series).

It then follows that this constant must be an integer since l and k are. ##\lambda_n=n\geq l+1##.

I would like to know the physical reason why the quantum number n arises and why it is put under the constraint ##n\geq l+1##.

Thank you for your time.

During the process a constant ##\lambda_n=\frac{ze^2}{4\pi\epsilon_0\hbar}(\frac{\mu}{2|E_n|})^{\frac{1}{2}}## is introduced, where mu represents the reduced mass of the electron.

Later this constant is put on the following restriction so that the power series has a finite power; ##\lambda_n=l+k+1## (where k is the index number for the power series).

It then follows that this constant must be an integer since l and k are. ##\lambda_n=n\geq l+1##.

I would like to know the physical reason why the quantum number n arises and why it is put under the constraint ##n\geq l+1##.

Thank you for your time.

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