A note on the Moll-Arias de Reyna integral

Producción CientíficaThe Moll-Arias de Reyna integral is generalized and several values are given.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León (project VA057U16

A relativistic one dimensional band model with position dependent mass

Producción CientíficaIn this note a one-dimensional band model is proposed based on a periodic Dirac comb having a periodic mass distribution m(x). The mass function is represented as a Hermitian, non-local separable operator. Two specific cases–a constant mass model and a sinusoidal mass model–are examined. The lowest electron and positron bands for the constant mass case are similar to those for the standard relativistic Kronig-Penney model, suggesting that non-locality has little influence. The results for the sinusoidal case are consistent with the expectation that at low wavenumber an electron “feels” it has an average constant mass, but at high wave number, the particle “sees” the periodic mass variation and the band is distorted.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León (project VA057U16