58 research outputs found
Using mixed data in the inverse scattering problem
Consider the fixed- inverse scattering problem. We show that the zeros
of the regular solution of the Schr\"odinger equation, , which are
monotonic functions of the energy, determine a unique potential when the domain
of the energy is such that the range from zero to infinity. This
suggests that the use of the mixed data of phase-shifts
, for which the zeros of the regular solution are monotonic in both domains,
and range from zero to infinity, offers the possibility of determining the
potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum
Scattering Theory, Hungary, August 200
Piecewise constant potentials and discrete ambiguities
This work is devoted to the study of discrete ambiguities. For parametrized
potentials, they arise when the parameters are fitted to a finite number of
phase-shifts. It generates phase equivalent potentials. Such equivalence was
suggested to be due to the modulo uncertainty inherent to phase
determinations. We show that a different class of phase-equivalent potentials
exists. To this aim, use is made of piecewise constant potentials, the
intervals of which are defined by the zeros of their regular solutions of the
Schr\"odinger equation. We give a classification of the ambiguities in terms of
indices which include the difference between exact phase modulo and the
numbering of the wave function zeros.Comment: 26 pages Subject: Mathematical Physics math-p
Zero modes in a system of Aharonov-Bohm fluxes
We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm
fluxes in the case when the solenoids are arranged in periodic structures like
chains or lattices. We also consider perturbations to such periodic systems
which may be infinite and irregular but they are always supposed to be
sufficiently scarce
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