The properties of the adiabatic representation of a multichannel Schrodinger equation are analyzed by exploiting the Hamiltonian and symplectic nature of the coefficient and transformation matrices, respectively. Use of this algebraic structure of the problem is shown to be in line with an approach developed by Fano and Klar [Klar and Fano, Phys. Rev. Lett. 37, 1132 (1976); Klar, Phys. Rev. A 15, 1452 (1977)] in their introduction of the postadiabatic potentials. The formal calculations due to Klar and Fano which halve the order of the matrices involved are given a rigorous mathematical background and described in a more general setup from the viewpoint of the theory of Hamiltonian and symplectic linear operators. An infinite sequence of postadiabatic representations is constructed and an algorithm for the choice of a symplectic transformation matrix for each representation is proposed. The interaction of fluorine atoms with hydrogen halides is considered as an example: In these cases, it is found that the first-postadiabatic representation shows lower coupling than the adiabatic one, and this provides a proper choice for a decoupling approximation. The present results, and in particular the recipes for obtaining the eigenvalues and eigenvectors of relevant matrices manipulating matrices of half the size, offer interesting perspectives for the numerical integration of multichannel Schrodinger equations.

Adiabatic and post-adiabatic representations for multichannel Schroedinger equations

AQUILANTI, Vincenzo;CAVALLI, Simonetta;
1994

Abstract

The properties of the adiabatic representation of a multichannel Schrodinger equation are analyzed by exploiting the Hamiltonian and symplectic nature of the coefficient and transformation matrices, respectively. Use of this algebraic structure of the problem is shown to be in line with an approach developed by Fano and Klar [Klar and Fano, Phys. Rev. Lett. 37, 1132 (1976); Klar, Phys. Rev. A 15, 1452 (1977)] in their introduction of the postadiabatic potentials. The formal calculations due to Klar and Fano which halve the order of the matrices involved are given a rigorous mathematical background and described in a more general setup from the viewpoint of the theory of Hamiltonian and symplectic linear operators. An infinite sequence of postadiabatic representations is constructed and an algorithm for the choice of a symplectic transformation matrix for each representation is proposed. The interaction of fluorine atoms with hydrogen halides is considered as an example: In these cases, it is found that the first-postadiabatic representation shows lower coupling than the adiabatic one, and this provides a proper choice for a decoupling approximation. The present results, and in particular the recipes for obtaining the eigenvalues and eigenvectors of relevant matrices manipulating matrices of half the size, offer interesting perspectives for the numerical integration of multichannel Schrodinger equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/111997
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