Instead of a potential given like $V(r) = k r^2$ or $V(r) = y^2$ , if the potential is given like in the form a function but not clearly specified, can we tell that if that commutes with the hamiltonian or not?
For example: We have given a potential $V(x^2 +y^2)$ and if we want to know if this commutes with any operator, for example angular momentum $L_z$, can we say that?
The reason I'm saying is because I think I could deal with the commutation if it is specified like,
$V(r)= 1 / r^2$ or $V(r)= r^2 +5\times1 / r^2$
I need to learn how I can deal with the unspecified function.