Related papers: Hearing the shape of a quantum boundary condition

Hearing the shape of a quantum boundary condition

URL: http://arxiv.org/abs/2204.10248v1
Date: Thu, 21 Apr 2022 16:33:13 GMT
Title: Hearing the shape of a quantum boundary condition
Authors: Giuliano Angelone, Paolo Facchi, Giuseppe Marmo
Abstract summary: We study the isospectrality problem for a free quantum particle confined in a ring with a junction. We classify the self-adjoint realizations in two classes, identifying all the families of isospectral Hamiltonians.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study the isospectrality problem for a free quantum particle confined in a ring with a junction, analyzing all the self-adjoint realizations of the corresponding Hamiltonian in terms of a boundary condition at the junction. In particular, by characterizing the energy spectrum in terms of a spectral function, we classify the self-adjoint realizations in two classes, identifying all the families of isospectral Hamiltonians. These two classes turn out to be discerned by the action of parity (i.e. space reflection), which plays a central role in our discussion.

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