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arXiv · 1202.1962

Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle

Sumit Ghosh
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Abstract

We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP. Apart from the forbidden band within the range $\pm m$, $m$ being the mass of the particle, we find the existence of additional forbidden bands at the both ends of the spectrum. Such band structure forbids a Dirac particle to penetrate a potential step of sufficient height ($\sim E_P$, $E_P$ being Planck energy). This is also true for massless particle. Unlike the relativistic case, a massless particle also can reflect from a barrier of sufficient height. Finally we discuss about the Klein's paradox in presence of the GUP.

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Sumit Ghosh. 2012-02-09. Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle. https://doi.org/10.1007/s10773-014-2265-8

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