Interplay between Riccati, Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum. (6th June 2018)

• Record Type: Journal Article
• Authors: Blanco‐Garcia, Zurika; Rosas‐Ortiz, Oscar; Zelaya, Kevin
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 4925
• Page End: 4938
• Publication Date: 2018-06-06
• Subjects: general mathematical topics and methods in quantum theory -- non‐selfadjoint operator theory in quantum theory -- quantum theory -- supersymmetry and quantum mechanics; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5069
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Nonlinear Riccati and Ermakov equations are combined to pair the energy spectrum of 2 different quantum systems via the Darboux method. One of the systems is assumed Hermitian, exactly solvable, with discrete energies in its spectrum. The other system is characterized by a complex‐valued potential that inherits all the energies of the former one and includes an additional real eigenvalue in its discrete spectrum. If such eigenvalue coincides with any discrete energy (or it is located between 2 discrete energies) of the initial system, its presence produces no singularities in the complex‐valued potential. Non‐Hermitian systems with spectrum that includes all the energies of either Morse or trigonometric Pöschl‐Teller potentials are introduced as concrete examples.