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## 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

[itex]H |n> = E_n |n>[/itex]

So:

[itex]<n| H = <n| E_n[/itex]

H is Hermitian.

So: Why is this?

## The Attempt at a Solution

I don't know if this is valid.

[itex](H \cdot |n>)^\dagger = (E_n \cdot |n>)^\dagger[/itex]

[itex]\Leftrightarrow[/itex]

[itex]<n| H^\dagger = <n| E_n^\dagger[/itex]

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

[itex]<n| H = <n| E_n[/itex]

Is this how things work?