I wanna see a pair of two unbounded positive and self-adjoint operators $A$ and $B$ (if one operator is bounded is even better) such that $AB-BA$ is unbounded. I guess
if $A$ is a second order differential operator on some appropriate domain and $B$ is a multiplication operator, then this is perhaps enough. I would like you to confirm this and why not give a better visualised example.
Thanks and I hope you'll be great as usual.
Math.