We study the eigenvalues of the two-dimensional Schrödinger operator with a large constant magnetic field perturbed by a decaying scalar potential. For each Landau level, we give the precise asymptotic distribution of eigenvalues created by the minimum, maximum and the closed energy curve of the potential. Normal form reduction, WKB construction and pseudodifferential calculus are applied to the effective Hamiltonian.

中文翻译：

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具有强磁场的二维Schrödinger算子的特征值和特征函数

我们研究具有恒定标磁场的二维Schrödinger算子的特征值，该恒定磁场受到标量势的衰减。对于每个Landau水平，我们给出了由电势的最小，最大和闭合能量曲线创建的特征值的精确渐近分布。正规形式约简，WKB构造和伪微积分被应用到有效的哈密顿量。