https://doi.org/10.1140/epjp/s13360-024-04923-8
Regular Article
Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal
interactions
1
Dipartimento di Science Ingegneristiche, Università of degli Studi Guglielmo Marconi, Via Plinio 44, 00193, Rome, Italy
2
Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011, Valladolid, Spain
c
luismiguel.nieto.calzada@uva.es
Received:
21
July
2023
Accepted:
19
January
2024
Published online:
6
February
2024
The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal attractive -interactions of equal strength and symmetrically located with respect to the origin. We use the procedure known as renormalisation of the coupling constant in order to rigorously achieve a self-adjoint determination for this Hamiltonian. This model depends on two parameters, the interaction strength and the distance between the centre of each interaction and the origin. Once we have the self-adjoint determination, we obtain its discrete spectrum showing that it consists of two negative eigenvalues representing the energy levels. We analyse the dependence of these energy levels on the above-mentioned parameters. We investigate the possible resonances of the model. Furthermore, we analyse in detail the limit of our model as the distance between the supports of the two
interactions vanishes.
© The Author(s) 2024
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