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arXiv · 2505.16913

Quantum Systems with jump-discontinuous mass. I

Fabio Deelan Cunden·Giovanni Gramegna·Marilena Ligabò
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Abstract

We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by the boundary conditions at the points of mass discontinuity. For a family of scale-free boundary conditions, we analyse the associated spectral problem. We find that the eigenfunctions exhibit a highly sensitive and erratic dependence on the energy. Notably, the system supports infinitely many distinct semiclassical limits, each labeled by a point on a spectral curve embedded in the two-torus. These results demonstrate a rich interplay between discontinuous coefficients, boundary data, and spectral asymptotics.

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Fabio Deelan Cunden, Giovanni Gramegna, Marilena Ligabò. 2025-05-22. Quantum Systems with jump-discontinuous mass. I. https://doi.org/10.1088/1361-6544%2Fae4afb

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