Dispersion relation of Bloch function and Landau diamagnetism

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Other Title
  • ブロッホ関数分散式とランダウ反磁性
  • ブロッホ カンスウ ブンサンシキ ト ランダウ ハンジセイ

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The possibility of anomalous Landau diamagnetism caused by anomalous dispersion relation in Bloch functions is examined. For this purpose the general restriction on the dispersion relation of Bloch function is investigated in one dimensional case. The analogy between the wave equation as a function of x and the mechanical equation as a function of time is utilized. By the aid of Lagrangean action integral, variations of some important integrals are estimated. The conclusion is given that the derivative of the energy by the momentum exactly equals the current of one electron. The exact relation, although evident in the case of free electron, imposes a rather strict restriction on the dispersion relation of Bloch function.

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