Quantum state where uncertainty in kinetic energy is zero?

While reading Shankar's book on Quantum Mechanics, I encountered an interesting problem:

Compute $\Delta T\cdot\Delta X$, where $T = P^2/2m$.

I found several solutions online which arrive at the result $\Delta T\cdot\Delta X \ge 0$.

My question is: does there exist a state $|{\psi}\rangle$ which saturates this inequality, i.e. for which $\Delta T\cdot\Delta X = 0$? We know $\Delta X\ne 0$ (from the uncertainty relation between $X$ and $P$), so then we must surely have that $\Delta T = 0$. But I'm struggling to imagine a physical state with a well-defined kinetic energy! If it is indeed possible, please provide an example of such a state. Thanks!