Iterative solutions of the close‐coupled equations that appear in the problem of rotational excitation of a rigid rotor

1974 ◽  
Vol 60 (11) ◽  
pp. 4520-4524 ◽  
Author(s):  
K. Nanbu
Keyword(s):  
Rigid Rotor ◽  
Rotational Excitation ◽  
Coupled Equations ◽  
Iterative Solutions

scholarly journals A Numeric Solution of the Quantum Rigid Rotor

2020 ◽  
Author(s):  
Guilherme de Souza Tavares de Morais ◽  
Rogério Custodio
Keyword(s):  
Grid Method ◽  
Integral Form ◽  
Rigid Rotor ◽  
Coordinate Systems ◽  
Numerical Techniques ◽  
Coupled Equations ◽  
Curvilinear Coordinate ◽  
Numeric Solution ◽  
Transformation Of Variables ◽  
Rotor Model

The Variable Fixed Grid Method (VFGM) combines numerical techniques of differentiation and integration to solve the Schrödinger equation in its integral form. The method is extremely simple and allows to overcome difficulties found in conventional resolutions and when coupled equations are produced. However, difficulties arise when curvilinear coordinate systems are used because there are no well-defined boundary conditions for the angular functions. Systematic numerical alternatives were performed using the rigid rotor model. A transformation of variables proved to be efficient for calculating energy and the wave function. The difficulties are located at the poles where the Jacobian of the curvilinear coordinate system is canceled. The method used in this work allows a greater application of VFGM for systems in different curvilinear coordinate systems.

Classical Study of Rotational Excitation of a Rigid Rotor: Li+ + H2

1971 ◽  
Vol 55 (12) ◽  
pp. 5499-5516 ◽  
Author(s):  
Robert A. La Budde ◽  
Richard B. Bernstein
Keyword(s):  
Rigid Rotor ◽  
Rotational Excitation ◽  
Classical Study

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

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