##### 4.1.3.1 So­lu­tion harmc-a

Ques­tion:

Ver­ify that the sets of quan­tum num­bers shown in the spec­trum fig­ure 4.1 do in­deed pro­duce the in­di­cated en­ergy lev­els.

An­swer:

The generic ex­pres­sion for the en­ergy is

or defin­ing ,

Now for the bot­tom level, 0, so 0, this state has en­ergy .

Sim­i­larly, in each of the three sets of the sec­ond en­ergy level in fig­ure 4.1, the three quan­tum num­bers , , and add up to 1, giv­ing this state en­ergy .

For the third en­ergy level, the three quan­tum num­bers of each set add up to 2, giv­ing en­ergy , and for the fourth set, the quan­tum num­bers in each of the ten sets add up to 3 for an en­ergy .