A singular one-dimensional bound state problem and its degeneracies
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Tarih
2017-08-01
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Yayıncı
Springer Verlag
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 (?A= ?A). 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 ? 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. © 2017, Società Italiana di Fisica and Springer-Verlag GmbH Germany.
Açıklama
Anahtar Kelimeler
Kaynak
European Physical Journal Plus
WoS Q Değeri
Q2
