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arXiv · 1805.05280

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

Federica Gregorio·Joachim Kerner
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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].

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Federica Gregorio, Joachim Kerner. 2018-05-14. On Lennard-Jones-type potentials on the half-line. https://doi.org/10.1007/s00013-018-1243-4

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