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## Main Question or Discussion Point

So im working up to some exams and have a question regarding properties of hermitians, specifically the properties of Hamiltonian operators and trying to prove that for example if..

[tex]\hat{O}[/tex] is a hamiltonian operator then...

[tex]\hat{O}[/tex] + [tex]\hat{O}[/tex][tex]\dagger[/tex]

is hermitian*.

Now what I think im having a problem with is understanding exactly what im expected to know with regard to this, as what I know about hamiltonian operators (real eigenvalues and orthogonality) don't seem to help a massive amount here (unless im meant to show that [tex]\hat{O}[/tex] with [tex]\hat{O}[/tex][tex]\dagger[/tex] is orthogonal).

Any help is appreciated, I feel this is one of them subjects where if I start to understand with one example like this I will be able to nail the rest out pretty quickly :)

*In case im explaining badly due to my limited knowledge of hermitian and hamiltonian things, the exact question says...

Show for any operator [tex]\hat{O}[/tex], that [tex]\hat{O}[/tex] + [tex]\hat{O}[/tex][tex]\dagger[/tex] is Hermitian.

edit: sigh, spelt the title wrong :(

[tex]\hat{O}[/tex] is a hamiltonian operator then...

[tex]\hat{O}[/tex] + [tex]\hat{O}[/tex][tex]\dagger[/tex]

is hermitian*.

Now what I think im having a problem with is understanding exactly what im expected to know with regard to this, as what I know about hamiltonian operators (real eigenvalues and orthogonality) don't seem to help a massive amount here (unless im meant to show that [tex]\hat{O}[/tex] with [tex]\hat{O}[/tex][tex]\dagger[/tex] is orthogonal).

Any help is appreciated, I feel this is one of them subjects where if I start to understand with one example like this I will be able to nail the rest out pretty quickly :)

*In case im explaining badly due to my limited knowledge of hermitian and hamiltonian things, the exact question says...

Show for any operator [tex]\hat{O}[/tex], that [tex]\hat{O}[/tex] + [tex]\hat{O}[/tex][tex]\dagger[/tex] is Hermitian.

edit: sigh, spelt the title wrong :(

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