As has been [remarked earlier](https://physics.stackexchange.com/questions/88267/why-delta-x-delta-p-x-for-stationary-states-increase-linearly-with-n), if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$ of the eigenstate, then for the two usual unbounded potentials (the simple harmonic oscillator and the infinite square well) $\Delta x\Delta p$ grows linearly with $n$.

How does this product behave for other solvable potentials, such as the linear cone potential $V(x)=|x|$?