- #1

Bunting

- 85

- 0

So I am 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 I am having a problem with is understanding exactly what I am 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 I am 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 I am 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 I am having a problem with is understanding exactly what I am 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 I am 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 I am 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 :(

Last edited: