Calculating resonance positions and widths using the Siegert approximation method

• Published in: European journal of physics Vol. 32; no. 5; pp. 1199 - 1211
• Main Author: Rapedius, Kevin
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.09.2011; Institute of Physics Publishing; Institute of Physics
• Subjects: Approximation; College Science; Communication, education, history, and philosophy; Comparative Analysis; Complement; Computation; Decay; Energy; Equations (Mathematics); Exact sciences and technology; General physics; Mathematical analysis; Mathematical models; Nonlinearity; Particles (of physics); Physics; Physics literature and publications; Probability; Quantum Mechanics; Schroedinger equation; Science Instruction; Scientific Concepts; Surveys and tutorial papers, resource letters; Tunnelling; Complex domain; Higher education; Semiclassical approximation; Positions; Schroedinger equation; Resonance; Physics; Trapped particle
• ISSN: 0143-0807; 1361-6404; 1361-6404
• DOI: 10.1088/0143-0807/32/5/008

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schrodinger equations. This approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations. (Contains 1 table and 1 figure.)