C. Filgueiras, E. O. Silva, F. M. Andrade
In this paper we investigate the bound state problem of quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we compare and discuss the results which come from the Schr\"{o}dinger and Dirac theories. The main difference between both theories is the presence/absence of a potential which contains the mean curvature of a given surface. This fact changes the dependence of the bound states on the angular momentum $l$. Moreover, there are bound states that are absent in the Dirac theory, in contrast with the Schr\"{o}dinger one, where they appear.
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http://arxiv.org/abs/1205.1155
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