Inconsistent operator-state relation in Zettili problems 3.4 and 3.5

[KostasV]

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.

Homework Equations

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?

 

[blue_leaf77]

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 $\hat{A}$.

 

[KostasV]

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]

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?

Yeah, probably.

 

[KostasV]

Yeah, probably.

Thanks for your response to my issue !