Gamow-Siegert functions and Darboux-deformed short range potentials
arXiv:0810.5597 · doi:10.1016/j.aop.2007.11.002
Abstract
Darboux-deformations of short range one-dimensional potentials are constructed by means of Gamow-Siegert functions (resonance states). Results include both Hermitian and non-Hermitian short range potentials which are exactly solvable. As illustration, the method is applied to square wells and barriers for which the transmission coefficient is a superposition of Fock-Breit-Wigner distributions. Resonance levels are calculated in the long lifetime limit by means of analytical and numerical approaches. The new complex potentials behave as an optical device which both refracts and absorbs light waves.
20 pages, 15 figures, LaTeX file
References in corpus (13)
- Schrödinger operators with complex potential but real spectrum
- SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
- The finite difference algorithm for higher order supersymmetry
- A Pedestrian Introduction to Gamow Vectors
- Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
- Second order SUSY transformations with `complex energies'
- Nonlocal supersymmetric deformations of periodic potentials
- Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
- Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
- The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential
- Quantum mechanical spectral engineering by scaling intertwining
- Irreducible second order SUSY transformations between real and complex potentials
- Exact propagators for complex SUSY partners of real potentials
Cited by in corpus (12)
- New supersymmetry-generated complex potentials with real spectra
- Resonances and antibound states of Pöschl-Teller potential: Ladder operators and SUSY partners
- Trends in supersymmetric quantum mechanics
- Wronskian differential formula for confluent supersymmetric quantum mechanics
- The rigged Hilbert space approach to the Gamow states
- Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
- Leaky modes of waveguides as a classical optics analogy of quantum resonances
- Complex oscillator and Painlevé IV equation
- The hyperbolic step potential: Antibound states, SUSY partners and Wigner time delays
- Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
- Extended WKB method, resonances and supersymmetric radial barriers
- Negative time delay for wave reflection from a one-dimensional semi-harmonic well