Singular spin-flip interactions for the 1D Schrödinger operator

2019/07/16 by Vladimir Kulinskii, Kulinskii, Vladimir, Dmitry Panchenko +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1907.06893

arxiv created 2019/08/06 · arxiv updated 2019/08/07

Abstract

We consider singular self-adjoint extensions for one-dimensional Schrödinger operator for two-component wave function within the framework of the distribution theory for discontinuous test functions \citefuncan_deltadistr_kurasov_jmathan1996. We show that among \mathdsC⁴-parameter set of boundary conditions with state mixing there is only \mathdsR²-parameter subset compatible with the spin interpretation of the two-component structure of the wave function. For the spin interpretation of such 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 which couples the electrical field inhomogeneity to spin.

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