Hi all,
When I study solid state physics, an equation and its derivation process make me very confused. In a nut shell, during the process author use H|ψn>=En|ψn>, which is easy to understand; however, he also used
H is an operator and can only act on bra vector from the right side. But E is a number, and because we use the linear algebra, it can be moved around freely:
)=(E=E()
Dear Alexander,
Thank you for your answer, but I still confused about the progress.
The whole equation in literature is:
++=dEn/dλ*δmn
which is obtained by derive operator H by λ.
And in book page on attachment it becomes:
En++Em=dEn/dλ*δmn
The first term, become En follows what you say, but the third term, becomes Em.
This means that operator can act on both side. However, it should not be a mistake of author since I have seen this theorem in other books as well. But I don't know what point I miss.
Dear Yixian,
This is a bit different question. Here you have to go back to 8.35, which in fact can be written both in form
H|ψn>=En|ψn>
and
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