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Citation - WoS: 2
Citation - Scopus: 3
Renormalization of Dirac Delta Potentials Through Minimal Extension of Heisenberg Algebra
(IOP Publishing Ltd., 2017) Erman, Fatih
We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other regularization schemes given in the literature.
Citation - WoS: 16
Citation - Scopus: 16
A Singular One-Dimensional Bound State Problem and Its Degeneracies
(Springer Verlag, 2017) Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, Haydar
We give a brief exposition of the formulation of the bound state problem for the one-dimensional system of N attractive Dirac delta potentials, as an N× N matrix eigenvalue problem (ΦA= ωA). The main aim of this paper is to illustrate that the non-degeneracy theorem in one dimension breaks down for the equidistantly distributed Dirac delta potential, where the matrix Φ becomes a special form of the circulant matrix. We then give elementary proof that the ground state is always non-degenerate and the associated wave function may be chosen to be positive by using the Perron-Frobenius theorem. We also prove that removing a single center from the system of N delta centers shifts all the bound state energy levels upward as a simple consequence of the Cauchy interlacing theorem.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection