Time-dependent resonant tunnelling

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Abstract
Two recent publications by Ricco and co-workers (1970, 1975) have drawn attention to important consequences that can arise when electrons tunnel through barriers which contain resonant states. The authors reason that there is then the possibility of close to 100% transmission for electrons which are on resonance. Their arguments are based on time-independent solutions of Schrodinger's equation. In this paper their discussion is supplemented by examining the time-dependent solution of a simplified version of their model. In particular an expression is found for the time it takes for an incident pulse to build up on penetrating into the well, and this is combined with an examination of the effect of the Fermi-Dirac statistics for electrons (orthogonal one-electron wavefunctions), both of which are relevant to the question of whether, in an actual experimental arrangement, these high transmissions are to be expected.

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