  We give an explicit correspondence between the domains of the self-adjoint
extensions of a one-dimensional Schr\"odinger 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.
