##### 4.4.2.1 So­lu­tion esdb-a

Ques­tion:

The 2p pointer state of the hy­dro­gen atom was de­fined as

What are the ex­pec­ta­tion val­ues of en­ergy, square an­gu­lar mo­men­tum, and an­gu­lar mo­men­tum for this state?

An­swer:

Note that the square co­ef­fi­cients of the eigen­func­tions and are each , so each has a prob­a­bil­ity in the 2p state.

Eigen­func­tion has an en­ergy eigen­value , and so does , so the ex­pec­ta­tion value of en­ergy in the 2p state is

This is as ex­pected since the only value that can be mea­sured in this state is .

Sim­i­larly, eigen­func­tion has a square an­gu­lar mo­men­tum eigen­value , and so does , so the ex­pec­ta­tion value of square an­gu­lar mo­men­tum in the 2p state is that value,

Eigen­func­tion has a an­gu­lar mo­men­tum eigen­value , and has , so the ex­pec­ta­tion value of an­gu­lar mo­men­tum in the 2p state is

Mea­sure­ments in which the an­gu­lar mo­men­tum is found to be av­er­age out against those where it is found to be .