RT info:eu-repo/semantics/article
T1 The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity
A1 Albeverio, Sergio
A1 Fassari, Silvestro
A1 Gadella Urquiza, Manuel
A1 Nieto Calzada, Luis Miguel
A1 Rinaldi, Fabio
K1 Gaussian potential
K1 Birman-Schwinger operator
K1 Hilbert-Schmidt operator
K1 contact interaction
K1 quantum well
AB 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.
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40857
UL http://uvadoc.uva.es/handle/10324/40857
LA eng
NO Frontiers in Physics, 2019, vol. 7, 12
NO Producción Científica
DS UVaDOC
RD 01-mar-2025