The Double Well Potential and the Krönig-Penney Model

K. A. Chao, Björn Magnusson

Bruce H. J. McKellar, G. J. Stephenson

We analyze the barrier problem and the Kronig-Penney model for Dirac particles, paying attention to the Klein paradox and the nature of the potential. The ambiguities associated with the \ensuremath{\delta}-function limit are examined and the physically reasonable way to include \ensuremath{\delta}-function potentials in the Dirac-Kronig-Penney problem is identified.

Michel Rousseau, J. P. Mathieu

Hugh F Jones

We consider a complex periodic PT-symmetric potential of the Kronig-Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form $V=i(\sin x)^{2N+1}$, and in particular the absence of anti-periodic solutions. In this model we show explicitly why these solutions disappear as soon as $V^*(x)\neq V(x)$, and spell out the consequences for the form of the dispersion relation.

Ippei Danshita, Susumu Kurihara, Shunji Tsuchiya

With use of the Kronig-Penney model, we study the excitation spectrum of a Bose-Einstein condensate in a one-dimensional periodic potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum for arbitrary values of the lattice depth. We find that the excitation spectrum is gapless and linear at low energies, and that it is due to the anomalous tunneling of low-energy excitations, predicted by Kagan et al.