Ground-state oscillator probability beyond the turning points
= Ground-state oscillator probability beyond the turning points
The ground-state turning points are $\pm\sqrt{\hbar/(m\omega)}$. In dimensionless position $y=x\sqrt{m\omega/\hbar}$, the <probability> outside them is $(2/\sqrt\pi)\int_1^\infty e^{-y^2}\,dy=\operatorname{erfc}(1)\simeq0.15730$. This tail demonstrates that a bound quantum state need not be confined to its classically allowed region.