for energy eigenstates E 0 = 0 and E 1 = ± ± π π ℏ ℏ / Δ Δ t . The states | E 0 ⟩ and | E 1 ⟩ are unique up to degeneracy of the energy level E 1 and an arbitrary phase factor φ φ . This result is sharp, in that this state also satisfies the Margolus–Levitin bound, in that E avg = δ δ E and so t ⊥ ⊥ = ℏ ℏ π π / 2 E avg = ℏ ℏ π π / 2 δ δ E . This result establishes that the combined limits are strict: