Atoms confined by very thin layers
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článek v časopisejournal article
Peer-reviewed
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Autor
Tušek M.
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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 Schrödinger operator acting effectively in L^2(R^2N) whose potential part depends on a. Moreover, we prove that after an appropriate regularization this Schrödinger operator tends, again in the norm resolvent sense, to the Hamiltonian of a two-dimensional atom (with the three-dimensional Coulomb potential-one over distance) as a->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.
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- Publikační činnost ČVUT [1323]