Electron in a periodic lattice + DC electric field
In a tight-binding band E(k) = −2J cos(ka), an electric field F causes k to drift linearly: dk/dt = eF/ℏ. When k reaches the Brillouin zone edge (π/a), it Bragg-reflects back — a Bloch oscillation with period T_B = h/(eFa). The Wannier-Stark ladder: discrete energy levels spaced eFa apart. Real space: the wavepacket oscillates with amplitude Δx = 4J/(eF).