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 Generalized Uncertainty Principle and Klein Paradox


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We have studied the Klein paradox in presence of a new generalized uncertainty principle. We define a new momentum operator and derive the modified dispersion relation for a Dirac particle. Apart from the forbidden band within the range $+- m$, m being the mass of the particle,we find the existence of additional forbidden bands which cause the allowed energy bands to be localised within finite energy range. This band structure forbids a Dirac particle from penetrating a potential barrier of sufficient height which is estimated to be of the order of Planck energy ($E P$). This is also true for a massless particle. It reflects from the wall of a sufficiently high (~$E P$) potential like a massive particle does in nonrelativistic quantum mechanics. We propose this to be a signature of the existence of a minimum length and a maximum energy.



Author: Sumit Ghosh

Source: https://archive.org/



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