Can degenerate bound states occur in onedimensional quantum mechanics?
Abstract
We point out that bound states, degenerate in energy but differing in parity, may form in onedimensional quantum systems even if the potential is nonsingular in any finite domain. Such potentials are necessarily unbounded from below at infinity and occur in several different contexts, such as in the study of localised states in braneworld scenarios. We describe how to construct large classes of such potentials and give explicit analytic expressions for the degenerate bound states. Some of these bound states occur above the potential maximum while some are below. Various unusual features of the bound states are described and after highlighting those that are ansatz independent, we suggest that it might be possible to observe such paritypaired degenerate bound states in specific mesoscopic systems.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2007
 DOI:
 10.1209/02955075/80/30004
 arXiv:
 arXiv:0706.1135
 Bibcode:
 2007EL.....8030004K
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Theory
 EPrint:
 10 pages, 2 figures, to appear in Europhysics Letters