# Darboux transformation for the discrete Schr\"odinger equation

@article{Aktosun2018DarbouxTF, title={Darboux transformation for the discrete Schr\"odinger equation}, author={Tuncay Aktosun and Abdon E. Choque-Rivero and Vassilis G. Papanicolaou}, journal={arXiv: Mathematical Physics}, year={2018} }

The discrete Schr\"odinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment. The Darboux transformation formulas are derived from first principles showing how the potential and the wavefunction change when a bound state is added or removed from the discrete spectrum of the corresponding Schr\"odinger operator without changing the continuous spectrum. This is done by explicitly…

## 3 Citations

### BOUND STATES OF THE DISCRETE SCHRÖDINGER EQUATION WITH COMPACTLY SUPPORTED POTENTIALS

- Mathematics
- 2019

The discrete Schrödinger operator is considered on the half-line lattice n ∈ {1, 2, 3, . . . } with the Dirichlet boundary condition at n = 0. It is assumed that the potential belongs to class Ab,…

### On the bound states of the discrete Schr\"odinger equation with compactly supported potentials

- Mathematics
- 2018

The discrete Schrodinger operator with the Dirichlet boundary condition is considered on the half-line lattice $n\in \{1,2,3,\dots\}.$ It is assumed that the potential belongs to class $\mathcal…

### Inverse problems for Jacobi operators with finitely supported perturbations

- Mathematics
- 2022

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse…

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The discrete Schrödinger operator is considered on the half-line lattice n ∈ {1, 2, 3, . . . } with the Dirichlet boundary condition at n = 0. It is assumed that the potential belongs to class Ab,…

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