I had a hard time understanding what it means to apply a symmetry operator to a function, so i wondered if there is a formal way to define this ?
As far as i understand it, applying a symmetry operation to a function means the followling:
\hat Rf(x) \rightarrow f(\hat Rx)
The result has then to be the same function with a coefficient in front of it. Otherwise it would not be symmetric in regard to the Symmetry Operator R.
Is this correct and can it be shown that this is how to apply symmetry operators to functions ?