1202.1962 (Sumit Ghosh)

Generalized Uncertainty Principle and Klein Paradox    [PDF]

Sumit Ghosh

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.

View original: http://arxiv.org/abs/1202.1962