Date(s) : 17/03/2020 iCal
11 h 00 min - 12 h 00 min
Discrete operators (i.e. difference operators) are often introduced as an approximation of
differential operators. However, if we start form the discrete model, it is not obvious that discrete
systems have continuum limits as the mesh size tends to 0. In this talk, we show that on physically
important lattices, e.g. the square, triangular, hexagonal lattices, the solutions for the stationary
Schroedinger equations associated to the continuous spectrum converge to those for the continuous
model. In particular, we can deal with graphen and graphite. Our solutions satisfy the radiation
condition, hence they describe the scattering phenomena. In the case of the hexagonal lattice, one can
derive both of Schroedinger equations and Dirac equations according to the energy.
This is a joint work with Arne Jensen in Aalborg.