A quantum particle in a symmetric double-well potential exhibits tunneling oscillations between the two wells. The wave packet oscillates with frequency Δ/ℏ, where Δ = E₊ − E₋ is the tunnel splitting — exponentially small in the barrier height.
Tunnel splitting: Δ ≈ ℏω₀ × exp(−√(2mV₀) × a/ℏ) — WKB formula
Time evolution: |ψ(t)⟩ = cos(Δt/2ℏ)|L⟩ + i·sin(Δt/2ℏ)|R⟩