We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length L, with N barriers of constant height V and width λ and N wells of width δ. In particular, we study the behaviour of the transmission coefficient in the limit N → ∞, with L fixed. This is achieved by letting δ and λ both scale as 1/N, in such a way that their ratio γ= λ/δ is a fixed parameter characterizing the model. In this continuum limit, the multi-barrier system behaves as it were constituted by a unique barrier of constant height E<inf>o</inf> = (γV)/(1 + γ). The analysis of the dispersion relation of the model shows the presence of forbidden energy bands at any finite N.

A continuum limit for the Kronig-Penney model

COLANGELI, MATTEO;
2015

Abstract

We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length L, with N barriers of constant height V and width λ and N wells of width δ. In particular, we study the behaviour of the transmission coefficient in the limit N → ∞, with L fixed. This is achieved by letting δ and λ both scale as 1/N, in such a way that their ratio γ= λ/δ is a fixed parameter characterizing the model. In this continuum limit, the multi-barrier system behaves as it were constituted by a unique barrier of constant height Eo = (γV)/(1 + γ). The analysis of the dispersion relation of the model shows the presence of forbidden energy bands at any finite N.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/111643
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