A Power Series Representation for the Characteristic Equation of Gamow-Siegert Eigenstates

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Barrera-Figueroa, V.^1

Instituto Politécnico Nacional, Sección de Estudios de Posgrado e Investigación, UPIITA, Av. Inst. Politec. Nal. 2580, Barrio la Laguna Ticoman, Ciudad de México

C.P. 07340, Mexico^1

关键词: Characteristic equation;    Dinger equation;    Energy parameters;    Explicit representation;    Numerical calculation;    Polynomial equation;    Power series;    Quantum system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012004/pdf
DOI  :  10.1088/1742-6596/839/1/012004

来源: IOP

【 摘 要 】

In this work we consider a quantum system described by a stationary Schrödinger equation and obtain an explicit representation for the characteristic equation of its Gamow-Siegert eigenstates in the form of a power series of the energy parameter. This representation is valid for both analytical or numerical calculations. We show that determining resonances reduces to calculating the roots of a polynomial equation. The effectiveness of this approach is demonstrated through several numerical examples.