2025/05/23 by Angelone, Giuliano, Asorey, Manuel, Ezquerro, Fernando +1
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.17920
We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy operator self-adjoint, and form a four-parameters family that includes the δ-potential and the δ'-potential as particular cases. We study the parameter dependence of the spectral properties of this system, finding a rich isospectrality structure. We systematically classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation.