Quick question about bra-ket notation

[Observer Two]

Homework Statement

On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say:

Homework Equations

H |n> = E_n |n>

So:

<n| H = <n| E_n

H is Hermitian.

So: Why is this?

The Attempt at a Solution

I don't know if this is valid.

(H \cdot |n>)^\dagger = (E_n \cdot |n>)^\dagger

\Leftrightarrow

<n| H^\dagger = <n| E_n^\dagger

And since H is Hermitian and E_n is real, I get:

<n| H = <n| E_n

Is this how things work?

 

[DrClaude]

That looks correct.

 

[Gamma]

Looks fine to me too.