Open AccessTruncated Radial Oscillators with a Bound State in the Continuum via Darboux Transformations
Author(s) -
L. López-Mejía,
Nicolás FernándezGarcía
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1540/1/012029
Subject(s) - bound state , eigenvalues and eigenvectors , angular momentum , mathematical physics , scattering , physics , square integrable function , wave function , integrable system , quantum mechanics , radius , transformation (genetics) , mathematical analysis , mathematics , biochemistry , chemistry , gene , computer security , computer science
The radial oscillator with zero angular momentum is used to construct a short-range model by cutting-off the potential at a given radius r = b , and by substituting it with a constant potential for r > b . The new potential, called truncated radial oscillator, admits both bound and scattering states. It is shown that the appropriate Darboux transformation leads to new exactly solvable models that have the entire energy spectrum of the truncated radial oscillator plus a new discrete energy eigenvalue. The latter defines a square-integrable wave function for the new system although it is embedded in the scattering regime of the energy spectrum. The new potentials are radial and such that their asymptotic behavior coincides with the profile predicted by von Neumann and Wigner for a potential to admit an eigenvalue in the continuum.