# 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} }

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…

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