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Using a variational approach, the interaction of an extrinsic electron with the surface modes of a semi-infinite medium is studied under the effect of an external magnetic field. The approach is to be valid for all values of the electron-surface-phonon coupling. In addition to the ground state energy, the number of phonons around the electron, and the spatial localization of the electron perpendicular and parallel to the surface are studied. It is observed that the magnetic field enhances the effective electron-phonon coupling and thus leads to an increased degree of localization of the electron toward the surface.

A Variational Approach for an Electron Interacting with an Impenetrable Dielectric Surface under the Effect of an External Magnetic Field