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Matrix Technique for Nonperturbative Green Function of Time-Independent Schrödinger Equation

Matrix Technique for Nonperturbative Green Function of Time-Independent Schrödinger Equation Abstract A Green function of time-independent multi-channel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multi-channel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multi-channel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multi-potential system within quasi-classical approximation. The limits of strong and weak inter-channel interactions are studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Matrix Technique for Nonperturbative Green Function of Time-Independent Schrödinger Equation

Pegarkov, Alexander I.
Acta Applicandae Mathematicae , Volume 84 (2): 29 – Nov 1, 2004
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References (13)

Publisher
Springer Journals
Copyright
2004 Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-004-5591-7
Publisher site
See Article on Publisher Site

Abstract

Abstract A Green function of time-independent multi-channel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multi-channel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multi-channel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multi-potential system within quasi-classical approximation. The limits of strong and weak inter-channel interactions are studied.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Nov 1, 2004

Keywords: Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization

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