This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumption that the magnetic field has a unique and non-degenerate minimum, we construct the local complex WKB approximations for eigenfunctions on a general surface. Furthermore, in the case of the Euclidean plane, with a radially symmetric magnetic field, the eigenfunctions are approximated in an exponentially weighted space.

中文翻译：

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表面上的磁性 WKB 结构

本文致力于通过复 WKB 方法描述磁拉普拉斯算子在半经典极限下的特征值和特征函数。在磁场具有唯一且非退化最小值的假设下，我们构造了一般表面上特征函数的局部复 WKB 逼近。此外，在欧几里得平面的情况下，具有径向对称磁场，本征函数在指数加权空间中近似。