Gamow vectors and Supersymmetric Quantum Mechanics

Abstract

Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single complex eigenvalue associated to normalized eigensolutions. These new Hamiltonians are not pseudo-hermitian operators and also differ from those obtained by means of complex-scaling transformations. As an example, Coulomb-like potentials are studied.

12 pages, 8 figures, LaTeX file

References in corpus (4)

• A Pedestrian Introduction to Gamow Vectors
• Second order SUSY transformations with `complex energies'
• Physical sectors of the confluent hypergeometric functions space
• The challenge of non-hermitian structures in physics

Cited by in corpus (6)

• New supersymmetry-generated complex potentials with real spectra
• Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
• Optical potentials using resonance states in Supersymmetric Quantum Mechanics
• On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms
• Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
• Extended WKB method, resonances and supersymmetric radial barriers