 01109 Pavel Exner, Katerina Nemcova
 Quantum mechanics of layers with a finite number of
point perturbations
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Mar 23, 01

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Abstract. We study spectral and scattering properties of a
spinless quantum particle confined to an infinite planar layer
with hard walls containing a finite number of point perturbations.
A solvable character of the model follows from the explicit form
of the Hamiltonian resolvent obtained by means of Krein's formula.
We prove the existence of bound states, demonstrate their
properties, and find the onshell scattering operator.
Furthermore, we analyze the situation when the system is put into
a homogeneous magnetic field perpendicular to the layer; in that
case the point interactions generate eigenvalues of a finite
multiplicity in the gaps of the free Hamiltonian essential
spectrum.
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