##### 4.3.4.2 So­lu­tion hydd-b

Ques­tion:

Check from the con­di­tions

that , , , and are the only states of the form that have en­ergy . (Of course, all their com­bi­na­tions, like 2p and 2p, have en­ergy too, but they are not sim­ply of the form , but com­bi­na­tions of the ba­sic so­lu­tions , , , and .)

An­swer:

Since the en­ergy is given to be , you have 2. The az­imuthal quan­tum num­ber must be a smaller non­neg­a­tive in­te­ger, so it can only be 0 or 1. In case 0, the ab­solute value of the mag­netic quan­tum num­ber can­not be more than zero, al­low­ing only 0. That is the state. In the case that 1, the ab­solute value of can be up to one, al­low­ing 1, 0, and 1.