najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-5-549-552najo-507Research ArticleMATHEMATICSМАТЕМАТИКАBound states for Laplacian perturbed by varying potential supportedby line in R3Связанные состояния лапласиана, возмущенного переменным потенциалом, сосредоточенным на линии в R3BagmutovA. S.BagmutovA. S.

Kronverkskiy, 49, Saint Petersburg, 197101

bagmutov94@mail.ruITMO UniversityRussian Federation202105082025125549552Copyright © Bagmutov A.S., 20252025Bagmutov A.S.Bagmutov A.S.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/507

We investigate a system with attracting δ-potential located along a straight line in 3D. It has constant intensity, except for a local region. We prove the existence of discrete spectrum and construct an upper bound on the number of bound states, using Birman-Schwinger method.

Мы исследуем систему с притягивающим дельта-потенциалом, сосредоточенным на прямой линии в R3 . Он постоянен, кроме ограниченной области. Мы доказываем существование дискретного спектра и строим верхнюю оценку количества связанных состояний, используя метод Бирмана-Швингера.

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The authors declare that there are no conflicts of interest present.