RT info:eu-repo/semantics/article
T1 A singular one-dimensional bound state problem and its degeneracies
A1 Erman, Fatih
A1 Gadella Urquiza, Manuel
A1 Tunali, Seçil
A1 Uncu, Haydar
K1 Dirac delta potential
K1 Potencial delta de Dirac
AB 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.
PB Springer
SN 2190-5444
YR 2017
FD 2017
LK http://uvadoc.uva.es/handle/10324/29265
UL http://uvadoc.uva.es/handle/10324/29265
LA eng
NO The European Physical Journal Plus, 2017, vol. 132. 19 p.
NO Producción Científica
NO Física Teórica. Atómica y Óptica
DS UVaDOC
RD 22-nov-2024