Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schrödinger operator in one dimension

Abstract

Physical realizations of non-standard singular self-adjoint extensions for one-dimensional Schrödinger 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.

11 pages, 7 figures

References in corpus (2)

• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Physical interpretation of point-like interactions of one-dimensional Schrödinger operator

Cited by in corpus (4)

• An approximation to the Woods-Saxon potential based on a contact interaction
• Band spectra of periodic hybrid $\delta$-${\delta }^{\prime }$ structures
• The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions