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
, where
is the principal quantum number
and will often be omitted,
is the total spin quantum number (
is the number of spin states),
refers to the orbital angular momentum quantum number
but is written
as
for
,
and
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 values for each .

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.

Jim Branson 2013-04-22