EDP Sciences Springer-Verlag 1998 Calculation of Wannier-Bloch and Wannier-Stark states

Abstract. The paper discusses the metastable states of a quantum particle in a periodic potential under a constant force (the model of a crystal electron in a homogeneous electric eld), which are known as the Wannier-Stark ladder of resonances. An ecient procedure to nd the positions and widths of resonances is suggested and illustrated by numerical calculations for a cosine potential, which are in excellent agreement with complex scaling resonance energies. PACS. 03.65.-w Quantum mechanics { 73.40.Gk Tunneling { 73.20.Dx Electron states in low-dimensional structures (superlattices, quantum well structures and multilayers)