Albeverio, Sergio

Fassari, Silvestro

Gadella Urquiza, Manuel

Nieto, Luis M.

Rinaldi, Fabio

Frontiers in Physics

English

arXiv

Producción CientíficaIn this note we consider a quantum mechanical particle moving inside an infinitesimally thin layer constrained by a parabolic well in the x-direction and, moreover, in the presence of an impurity modeled by an attractive Gaussian potential. We investigate the Birman-Schwinger operator associated to 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 bound states created by the impurity. Furthermore, we consider the case where the Gaussian potential degenerates to a δ-potential in the x-direction and a Gaussian potential in the y-direction. We construct the corresponding self-adjoint Hamiltonian and prove that it is the limit in the norm resolvent sense of a sequence of corresponding Hamiltonians with suitably scaled Gaussian potentials. Satisfactory bounds on the ground state energies of all Hamiltonians involved are exhibited.MIinisterio de Economía y Competitividad (MTM2014-57129-C2-1-P)Junta de Castilla y León/ FEDER (BU229P18, VA057U16, VA137G18

Nieto Calzada, Luis Miguel

Repositorio Documental de la Universidad de Valladolid

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

http://uvadoc.uva.es/bitstream/handle/10324/40857/fphy-07-00102%281%29.pdf?sequence=1&isAllowed=y

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

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Repositorio Documental de la Universidad de Valladolid