Atoms confined by very thin layers

作者：Tusek Matej^*

来源：Journal of Mathematical Physics, 2014, 55(11): 112105.

DOI：10.1063/1.4901560

The Hamiltonian of an atom with N electrons and a fixed nucleus of infinite mass between two parallel planes is considered in the limit when the distance a between the planes tends to zero. We show that this Hamiltonian converges in the norm resolvent sense to a Schrodinger operator acting effectively in L-2(R-2N) whose potential part depends on a. Moreover, we prove that after an appropriate regularization this Schrodinger operator tends, again in the norm resolvent sense, to the Hamiltonian of a two-dimensional atom (with the three-dimensional Coulomb potentialone over distance) as a -%26gt; 0. This makes possible to locate the discrete spectrum of the full Hamiltonian once we know the spectrum of the latter one. Our results also provide a mathematical justification for the interest in the two-dimensional atoms with the three-dimensional Coulomb potential.

• 出版日期2014-11