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arXiv · 1805.11136

Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schr\"odinger operator in one dimension

Vladimir Kulinskii·Dmitry Panchenko
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Abstract

Physical realizations of non-standard singular self-adjoint extensions for one-dimensional Schr\"odinger operator in terms of the mass-jump are considered. It is shown that corresponding boundary conditions can be realized for the Hamiltonian with the position-dependent effective mass in two qualitatively different profiles of the effective mass inhomogeneity: the mass-jump and the mass-bump. The existence of quantized magnetic flux in a case of the mass-jump is proven by explicit demonstration of the Zeeman-like splitting for states with the opposite projections of angular momentum.

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Vladimir Kulinskii, Dmitry Panchenko. 2018-05-28. Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schr\"odinger operator in one dimension. https://doi.org/10.1016/j.aop.2019.03.001

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