# What is mean by 'good quantum number' in spectroscopy?

In electronic spectroscopy of molecules, why some quantum numbers are considered to be 'good quantum numbers'? For example, $n$ and $l$ are said to be not good quantum numbers while $j$ is considered to be a 'good quantum number'. What is the logic/idea behind these concepts?

• Do you have any reference for the term? – Andreas H. Aug 20 '13 at 19:59

• @albedo Good quantum numbers are useful for labelling states. Recall that if you have $[H,A] = 0$ you can find simultaneous eigenstates of $H$ and $A$. That is, you have states with well defined energy and property $A$ (e.g. angular momentum). You couldn't do that if $[H,A] \neq 0$. – Goku Aug 22 '13 at 0:01
• @Goku: Then why $l$ is a good quantum number in closed shell atomic systems? $l$ is still not conserved right? [Reference: Annu.Phys.Rev.Chem.2003,54,397-424; in page 401]. – albedo Aug 25 '13 at 8:12
• @albedo I guess it is simply because in a closed shell $s=0$. Then we have $j=s+l=l$ conserved. – Goku Sep 13 '13 at 2:53
• If $[H,A]\neq0$ then the $A$ (e.g. angular momentum) is not good quantum number. This means if you have a state with specific energy, and you measure the angular momentum, you will get different values. – xslittlegrass Oct 4 '13 at 15:32