I have a couple of questions about selection rules for the hydrogen atom.(adsbygoogle = window.adsbygoogle || []).push({});

When we talk about these rules in an undergraduate context we are usually assuming LS coupling where we ignore spin orbit coupling so orbital and spin angular momentum are essentially independent. Is that correct?

Subsuming the basic l,m_l rules in this case we have

[tex]

\Delta J=\pm 1, \text{except J=0} \rightarrow J=0.

\\

\Delta m_j=\pm 1,0

\\

\Delta S=0 \text{ since the electron is always spin half}

\\

\text{but } \Delta m_s=\pm 1\text{ since we can transition from spin up to spin down?}

[/tex]

If we can indeed transition from spin up to spin down couldn't we possibly have [tex]\Delta m_j=\pm -2[/tex] from (m_l=1, up) to (m_l=0,down) then in violation of the above rule?

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# Selection Rules

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