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## Homework Statement

How do I show that the annihilation operator [tex] \hat{a} [/tex] is hermitian WITHOUT explicitly using the condition where an operator X is hermitian if its adjoint is also X ie. [tex] X=X^+ [/tex]

## Homework Equations

none.

## The Attempt at a Solution

I could show [tex] \hat{a} \hat{x} \neq \hat{x} \hat{a} [/tex] where [tex] \hat{x} [/tex] is the position operator, but that only shows non-hermiticity for that one operator...

Is there a more elegant way to show non-hermiticity simply?