The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schrödinger equations whose potentials are required to be shape invariant. Analytical solutions for the energy bound states are obtained for several magnetic fields. The associated spectrum is analyzed, and the probability and current densities are determined.

中文翻译：

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双层石墨烯中的电子，其磁场导致形状不变电势

解决了双层石墨烯中电子在施加磁场时的量子行为。通过使用二阶超对称量子力学，该问题转化为两个相互交织的一维平稳薛定r方程，其势能要求形状不变。对于几个磁场，获得了能量束缚态的解析解。分析相关的频谱，并确定概率和电流密度。