Electron in Bilayer Graphene with Magnetic Fields Associated with Solvable Potentials

The behavior of an electron in bilayer graphene with applied magnetic fields orthogonal to the surface is studied. By using second-order supersymmetric quantum mechanics some analytic solutions are found, which are expressed in terms of the eigenfunctions of two intertwined Schrodinger Hamiltonians. The case of a constant homogeneous magnetic field which leads to a pair of shifted harmonic oscillator potentials is discussed. A variant of this example produces inhomogeneous magnetic fields whose exact solutions for the electron motion in bilayer graphene are straightforwardly identified.