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arXiv · 1907.06893

Singular spin-flip interactions for the 1D Schr\"{o}dinger operator

Vladimir Kulinskii·Dmitry Panchenko
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Abstract

We consider singular self-adjoint extensions for one-dimensional Schr\"{o}dinger operator for two-component wave function within the framework of the distribution theory for discontinuous test functions \cite{funcan_deltadistr_kurasov_jmathan1996}. We show that among $\mathds{C}^{4}$-parameter set of boundary conditions with state mixing there is only $\mathds{R}^2$-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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Vladimir Kulinskii, Dmitry Panchenko. 2019-07-16. Singular spin-flip interactions for the 1D Schr\"{o}dinger operator. https://arxiv.org/abs/1907.06893

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