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    Título
    The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity
    Autor
    Albeverio, Sergio
    Fassari, SilvestroAutoridad UVA Orcid
    Gadella Urquiza, ManuelAutoridad UVA Orcid
    Nieto Calzada, Luis MiguelAutoridad UVA Orcid
    Rinaldi, Fabio
    Año del Documento
    2019
    Descripción
    Producción Científica
    Documento Fuente
    Frontiers in Physics, 2019, vol. 7, 12
    Résumé
    In 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.
    Palabras Clave
    Gaussian potential
    Birman-Schwinger operator
    Hilbert-Schmidt operator
    contact interaction
    quantum well
    Revisión por pares
    SI
    DOI
    10.3389/fphy.2019.00102
    Patrocinador
    MIinisterio de Economía y Competitividad (MTM2014-57129-C2-1-P)
    Junta de Castilla y León/ FEDER (BU229P18, VA057U16, VA137G18)
    Version del Editor
    https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00102/full
    Propietario de los Derechos
    © 2019 Albeverio, Fassari, Gadella, Nieto and Rinaldi
    Idioma
    eng
    URI
    http://uvadoc.uva.es/handle/10324/40857
    Tipo de versión
    info:eu-repo/semantics/publishedVersion
    Derechos
    openAccess
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    • FM - Artículos de revista [134]
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