Calculating resonance positions and widths using the Siegert approximation method

Abstract

Here we present complex resonance states (or Siegert states), that describe the tunneling decay of a trapped quantum particle, from an intuitive point of view which naturally leads to the easily applicable Siegert approximation method that can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schrödinger equation. Our approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations.

15 pages, 1 figure, contains MATLAB source code; new version with additional illustrations

References in corpus (5)

• Complex scaling approach to the decay of Bose-Einstein condensates
• Barrier transmission for the one-dimensional nonlinear Schrödinger equation: resonances and transmission profiles
• Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential

Cited by in corpus (6)

• The rigged Hilbert space approach to the Gamow states
• Revisiting double Dirac delta potential
• A Padé approximant approach to two kinds of transcendental equations with applications in physics
• Closed system approach to open systems: Tunneling decay of interacting cold bosons in an optical lattice
• Resonances for symmetric two-barrier potentials
• New shape resonances in one dimension