Answer to Question #163617 in Quantum Mechanics for Max

Question

Explain spectroscopic notation.

Answer 1

A common way to name states in atomic physics is to use spectroscopic notation. It is essentially a standard way to write down the angular momementum quantum numbers of a state. The general form is N^2s+1L_j, where N is the principal quantum number and will often be omitted, s is the total spin quantum number ( (2s + 1)  is the number of spin states), L  refers to the orbital angular momentum quantum number l but is written as S, P, D, F... for l = 0, 1, 2, 3... , and j is the total angular momentum quantum number.

A quick example is the single electron states, as we find in Hydrogen. These are:

All of these have the pre-superscript 2 because they are all spin one-half. There are two j values for each l.For atoms with more than one electron, the total spin state has more possibilities and perhaps several ways to make a state with the same quantum numbers.