A Primer on Resonances in Quantum Mechanics

Abstract

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

28 pages, 9 figures, lectures presented at the Advanced Summer School in Physics 2008, Cinvestav, Mexico

References in corpus (4)

• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• Quantum mechanical spectral engineering by scaling intertwining
• Optical potentials using resonance states in Supersymmetric Quantum Mechanics
• On first-order scaling intertwining in quantum mechanics

Cited by in corpus (9)

• Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
• Leaky modes of waveguides as a classical optics analogy of quantum resonances
• Transition from the wave equation to either the heat or the transport equations through fractional differential expressions
• Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
• Extended WKB method, resonances and supersymmetric radial barriers
• Negative time delay for wave reflection from a one-dimensional semi-harmonic well
• Fractional Driven Damped Oscillator
• Singularities of Floquet Scattering and Tunneling
• Scattering by infinitely rising one-dimensional potentials