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Theoretical considerations which pertain to electric currents through quantum‐well structures or finite superlattices in the presence of periodic time‐dependent applied potentials are presented. The paper includes (1) a time‐dependent generalization of the time‐independent, noninteracting electron, one‐dimensional potential model of Tsu and Esaki, (2) a derivation of generalized unitarity identities which relate all of the elastic and inelastic transitions which a particle can undergo when it interacts with a periodic time‐dependent, one‐dimensional, arbitrarily shaped potential barrier, and (3) an analysis of many‐body effects which reveals additional non‐Tsu‐Esaki current terms which disappear when the time‐dependent part of the applied potential is turned off. All of the results are expressed in terms of one‐particle scattering matrices which can be computed from the ordinary single‐particle, time‐dependent Schrödinger equation. This work may have high‐frequency device applications.