Eur. Phys. J. Plus (2018) 133: 251
https://doi.org/10.1140/epjp/i2018-12082-2

Regular Article

Novel connection between lump-like structures and quantum mechanics

¹ Departamento de Física, Universidade Federal da Paraíba, 58051-970, João Pessoa, PB, Brazil
² Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC, Universidad de Valencia, Burjassot-46100, Valencia, Spain

^* e-mail: bazeia@fisica.ufpb.br

Received: 9 March 2018
Accepted: 29 May 2018
Published online: 10 July 2018

Abstract

This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double well.