• Corpus ID: 218763445

Self-Adjoint extensions of the one-dimensional Schr\"odinger operator with symmetric potential

@article{Higuchi2020SelfAdjointEO,
  title={Self-Adjoint extensions of the one-dimensional Schr\"odinger operator with symmetric potential},
  author={Atsushi Higuchi and David Serrano Blanco},
  journal={arXiv: Mathematical Physics},
  year={2020}
}

• A. Higuchi, David Serrano Blanco
• Published 21 May 2020
• Mathematics
• arXiv: Mathematical Physics

We give an explicit correspondence between the domains of the self-adjoint extensions of a one-dimensional Schrodinger differential operator with symmetric real-valued potential and the boundary conditions the functions in the resulting domains must satisfy. As is well known, each self-adjoint extension is parametrized by a unitary matrix. We make the correspondence of this unitary matrix with the boundary conditions explicit, recovering the most familiar types of boundary conditions as special cases. We also demonstrate this correspondence implicitly for non-symmetric real-valued potential.