Interplay between Riccati, Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum

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 t...

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Vydané v:	Mathematical methods in the applied sciences Ročník 42; číslo 15; s. 4925 - 4938
Hlavní autori:	Blanco‐Garcia, Zurika, Rosas‐Ortiz, Oscar, Zelaya, Kevin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Freiburg Wiley Subscription Services, Inc 01.10.2019
Predmet:	Eigenvalues Energy spectra general mathematical topics and methods in quantum theory Mathematical analysis Nonlinear equations non‐selfadjoint operator theory in quantum theory quantum theory Schrodinger equation Singularity (mathematics) supersymmetry and quantum mechanics
ISSN:	0170-4214, 1099-1476
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.5069