1. The problem statement, all variables and given/known data On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say: 2. Relevant equations [itex]H |n> = E_n |n>[/itex] So: [itex]<n| H = <n| E_n[/itex] H is Hermitian. So: Why is this? 3. 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?