I need your opinions on Zettili's solution of an exercise

1. Homework Statement

(Uploaded photo from Zettili Quantum Mechanics - Chapter 3 - Solved problems 3.4 and 3.5)
Check at problem 3.4 the relation that he gives between operator A and state φn.
Now check the relation that he uses in problem 3.5 between A and φn again.
They are different while on the announcement of prob 3.5 he does not mention any change of this relation.

The Attempt at a Solution

Is there any misprint or am i that dumb that cannot understand some change of the relation that he implies?

Last edited:

blue_leaf77
Homework Helper
I think that's not a misprint for the answer of prob 3.5 follows as a consequence of the written relation between ##\hat{A}## and ##|\phi_n\rangle## in that problem. My guess is that he forgot that in the previous problem 3.4 he defined ##|\phi_n\rangle##'s as the eigenstates of ##\hat{A}##.

I think that's not a misprint for the answer of prob 3.5 follows as a consequence of the written relation between ##\hat{A}## and ##|\phi_n\rangle## in that problem. My guess is that he forgot that in the previous problem 3.4 he defined ##|\phi_n\rangle##'s as the eigenstates of ##\hat{A}##.

So, in problem 3.5 he probably wanted to change the relation between ##\hat{A}## and ##|\phi_n\rangle## to ##\hat{A}## ##|\phi_n\rangle## = n ##\alpha_o\ ## ##|\phi_{n+1}\rangle## (in order not to be anymore eigenstates of ##\hat{A}## ) but forgot to mention it?

blue_leaf77