The Kronig–Penney model is a model used to study properties of electrons confined in a periodic potential. It is a useful model since the electronic properties can be studied analytically with the aid of Bloch’s theorem. An important concept that emerges from the resultant electron band theory is the electron effective mass. Through the use of the Kronig–Penney model we use the so-called ‘effective mass theorem’, that allows us to ask and answer the question of how the electron effective mass depends on both the free electron mass and the characteristics of the periodic potential. We illustrate the crossover from the case of a weak periodic potential to a strong periodic potential using this theorem and explicit calculations with the Kronig–Penney model. The special case of the Dirac comb model is also treated in this work. Through the use of the ‘effective mass theorem’, we show, among other properties, that an electron–hole effective mass asymmetry is generally expected, even without considering contributions from electron–electron interactions.

Kronig-Penney模型是用于研究限制在周期性电势中的电子特性的模型。这是一个有用的模型，因为可以借助Bloch定理来分析电子性质。从合成电子能带理论中出现的一个重要概念是电子有效质量。通过使用Kronig-Penney模型，我们使用了所谓的“有效质量定理”，这使我们能够提出和回答电子有效质量如何同时依赖于自由电子质量和周期性电势特性的问题。 。我们使用该定理和克朗格-彭尼模型的显式计算，说明了从弱周期性势态到强周期性势态的转换。这项工作还处理了狄拉克梳子模型的特殊情况。