Abstract
The exact solutions of the Schr\odinger equation of a two-dimensional hydrogen molecular ion (2D HMI), expressed in confocal elliptic coordinates, are obtained. Calculated results show that the binding energy and equilibrium distance of the ground state of a 2D HMI are, respectively, much larger and shorter than those of a 3D HMI, and that the behavior of a low-dimensional electron is similar to that of a more massive charged particle. This may be useful for understanding new physical phenomena.
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