# The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

@article{Albeverio2019TheBO, title={The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity}, author={Sergio Albeverio and Silvestro Fassari and Manuel Gadella and Luis Miguel Nieto and Fabio Rinaldi}, journal={Frontiers in Physics}, year={2019} }

In this note we are concerned with the limiting case of a zero-thickness layer with harmonic conﬁnement along one of the two available dimensions. We investigate the Birman-Schwinger operator for such a model assuming the presence of a Gaussian impurity inside the layer and prove that such an integral operator is Hilbert-Schmidt, which allows the use of the modiﬁed Fredholm determinant in order to compute the impurity bound states. Furthermore, we consider the Hamiltonian H0 −λ√πδ(x)e−y2, that…

## 10 Citations

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S. Fassari, F. Rinaldi Department of Higher Mathematics, ITMO University, St. Petersburg, Russia CERFIM, PO Box 1132, CH-6601 Locarno, Switzerland Dipartimento di Fisica Nucleare, Subnucleare e delle…

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