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Continuous spectra of generalized Kronig-Penney model. (English) Zbl 1065.81055

Summary: The standard Kronig-Penney model with periodic \(\delta\) potentials is extended to the cases with generalized contact interactions. The eigen equation which determines the dispersion relation for one-dimensional periodic array of the generalized contact interactions is deduced with the transfer matrix formalism. Numerical results are presented which reveal unexpected band spectra with broader band gap in higher energy region for generic model with generalized contact interaction.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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