Abstract
We consider singular self-adjoint extensions of one-dimensional Schrödinger operator acting in space of two-component wave functions within the framework of the distribution theory (Kurasov 1996 J. Math. Anal. Appl. 201 297). We show that among -parameter set of boundary conditions with state mixing there is only -parameter subset compatible with the spin interpretation of the two-component structure of wave function. They can be identified as the point-like spin-momentum (Rashba) interactions. We suggest their physical realizations based on the regularized form of the Hamiltonian with coupling of the electrical field inhomogeneity of a background and spin of a carrier.
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