Year: 2026
Type: preprint
Abstract: This work provides a complete analytical characterization of the transfer- matrix structure associated with the finite Kronig-Penney model consisting of one-dimensional arrays of Dirac delta potentials recently introduced by Figueroa et al. (2025). Although their study identified the emergence of specific transfer-matrix entries and related combinatorial coefficients, a rig- orous derivation of the corresponding closed-form expressions has not yet been established. By expressing the N th power of the unit-cell transfer ma- trix in terms of Chebyshev polynomials of the second kind, we obtain explicit closed-form representations for the global transmission and reflection ampli- tudes. The proposed formulation reveals a previously unrecognized structural correspondence between multiple quantum scattering processes, discrete con- volutional patterns, and hypercomplex combinatorial structures.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212075998