• Corpus ID: 21732847

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… 

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