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Citation - WoS: 16
Citation - Scopus: 16
A Singular One-Dimensional Bound State Problem and Its Degeneracies
(Springer Verlag, 2017) Erman, Fatih; Erman, Fatih; Tunalı, Seçil; Uncu, Haydar; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
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.

Mathematics / Matematik