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On Lennard-Jones-type potentials on the half-line

By Federica Gregorio and Joachim Kerner

Abstract

In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the literature and due to its singularity at the origin it cannot be considered as a standard perturbation of the one-dimensional Laplacian. It is therefore our aim to provide a thorough description of the Hamiltonian in one dimension via the construction of a suitable quadratic form. Our results include a discussion of spectral and scattering properties which finally allows us to generalise some results from [Robinson1974] as well as [RadinSimon1978].Comment: various typos corrected; to appear in Archiv der Mathemati

Topics: Mathematical Physics, 81Q10, 81Q37, 81Q80, 81Q35, 47E05, 47D08
Publisher: 'Springer Science and Business Media LLC'
Year: 2018
DOI identifier: 10.1007/s00013-018-1243-4
OAI identifier: oai:arXiv.org:1805.05280

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