Klein Paradox

Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6 183-191 Katsnelson MI, Novoselov KS, Geim AK (2006) Chiral tunnelling and the Klein paradox in graphene. Nat Phys 2 620-625... 

For free particles this point of view has indeed some attractive features. There are, however, situations where the sign of the energy does not distinguish between electronic and positronic behavior. Consequently, transitions from electronic to positronic states cannot be excluded. A famous example is the Klein paradox, where a potential step divides space into two regions with a different interpretation of particles and antiparticles. If the step size is larger than twice... 

A very important practical matter in MBPT calculations is the efficient and accurate evaluation of sums such as encountered in 2- As a first step the atom is considered as being at the center of a large sphere that confines electrons within a radius R this serves to discretize the continuum states. Care must be taken with the boundary conditions to avoid the Klein paradox the electron mass, a scalar, rather than the potential is chosen to go to infinity for r > R. 72 is chosen to be large compared to the atom, typically around 72 = 50 — 70 a.u.. For a given value of the angular momentum quantum number k, the Dirac equation for an electron of energy e with upper and lower components 72c(r) and respectively, can be obtained by requiring 5S = 0, where... 

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