https://doi.org/10.1140/epjp/s13360-022-03065-z
Regular Article
Features of the bound state formation near a nonlinear defect in the presence of a homogeneous external field
1
Belgorod V. G. Shukhov State Technological University, Kostukova St., 46, 308012, Belgorod, Russia
2
Belgorod I. D. Putilin Legal Institute, Gorkogo St., 71, 308024, Belgorod, Russia
Received:
11
May
2022
Accepted:
12
July
2022
Published online:
28
July
2022
We find the exact solution to the non-relativistic time-independent Schrödinger equation with the homogeneous external field and the nonlinear δ-functional potential describing the point defect. The obtained solution describes the symmetrical bound states determined by the Airy function. We find the energy discrete spectrum of the bound states. The properties of bound states and energy level are analyzed in dependence on the system parameters such as the power of the defect, the intensity of the nonlinear response of the defect, and the external field intensity. We determine the effective power of defect. The bound states in the presence of an external field exist for both attractive and repulsive defects. We find the differences in the wave function profiles for attractive and repulsive defects. A decrease in the intensity of the external field leads to a decrease in the bound state energy. The presence of the defect leads to the formation of a ground state of a completely different structure, the wave function of which is characterized by two symmetrical maxima and one minimum. We find the bound state of a specific type, which can exist only near defect characterized by nonlinear response. The bound states of this type arise in the case of the zero effective power of defect corresponding to the situation when the influence of the linear and nonlinear responses of the defect compensates each other. Their existence is due to an external field that forms a triangular potential well.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
