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Quantum mechanical generalized phase-shift approach to atom-surface scattering: A Feshbach projection approach to dealing with closed channel effects

Maji, Kaushik ; Kouri, Donald J

The Journal of chemical physics, 2011-03, Vol.134 (12), p.124103-124103-12 [Periódico revisado por pares]

United States: American Institute of Physics

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Título:
Quantum mechanical generalized phase-shift approach to atom-surface scattering: A Feshbach projection approach to dealing with closed channel effects
Autor: Maji, Kaushik ; Kouri, Donald J
Assuntos: ALGORITHMS ; APPROXIMATIONS ; ATOMIC AND MOLECULAR PHYSICS ; ATOMS ; BOUNDARY CONDITIONS ; CALCULATION METHODS ; DEGREES OF FREEDOM ; DIFFERENTIAL EQUATIONS ; DISPERSIONS ; EQUATIONS ; FUNCTIONS ; HOMOGENEOUS MIXTURES ; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ; MATHEMATICAL LOGIC ; MATHEMATICAL OPERATORS ; MATHEMATICAL SOLUTIONS ; MATRICES ; MECHANICS ; MIXTURES ; NUMERICAL SOLUTION ; PARTIAL DIFFERENTIAL EQUATIONS ; PHASE SHIFT ; PROJECTION OPERATORS ; QUANTUM MECHANICS ; S MATRIX ; SCATTERING ; SCHROEDINGER EQUATION ; SOLUTIONS ; SURFACES ; TIME DEPENDENCE ; WAVE EQUATIONS ; WAVE FUNCTIONS
É parte de: The Journal of chemical physics, 2011-03, Vol.134 (12), p.124103-124103-12
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N 2 scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.
Editor: United States: American Institute of Physics
Idioma: Inglês

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Quantum mechanical generalized phase-shift approach to atom-surface scattering: A Feshbach projection approach to dealing with closed channel effects

Maji, Kaushik ; Kouri, Donald J

United States: American Institute of Physics

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