 Uncertainty product of oscillator number states

An energy eigenstate has $⟨x⟩=⟨p⟩=0$, $⟨x^2⟩=\hslash (n+1/2)/(m\omega )$ and $⟨p^2⟩=m\hslash \omega (n+1/2)$. Thus $\Delta x\Delta p=\hslash (n+1/2)$; only the ground state in this sequence minimizes the Heisenberg uncertainty principle.