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Il nuovo cimento

The theory of reactive (rearrangement) scattering for three atoms in three physical dimensions using adiabatically adjusting, principal axes hyperspherical (APH) coordinates is given. The relationships of the APH coordinates to Delves and Jacobi coordinates are given, and the kinetic energy operator is shown to be relatively simple. Procedures for solving the equations via either an exact coupled channel (CC) method or an optimum centrifugal sudden (CSAPH) approximation are given as well as procedures for applying scattering boundary conditions. Surface functions of two angles are obtained using a finite element method with an optimized, nonuniform mesh, and the CC equations are solved using the efficient VIVAS method. Sample CC results are given for the H3 system. The present approach has the advantages that all arrangements are treated fully equivalently; it is a principal axis system, so that both axes and internal coordinates swing smoothly with the reactions; it is directly applicable to both symmetric and unsymmetric systems and mass combinations and all total angular momenta; it gives convenient mappings for visualization of potential energy surfaces and wave functions; only regular radial solutions are required; all coordinate matching is by simple projection; and the expensive parts of the calculation are energy independent, so that, once they are done, the scattering matrices can be rapidly generated at the large numbers of energies needed to map out reactive thresholds and resonances. Accurate reactive scattering calculations are now possible for many chemically interesting reactions that were previously intractable.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

Preface Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one 2. Econophysics: statistical physics and social science 3. Quantum social science: a non-mathematical motivation Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries 5. Basic elements of quantum mechanics 6. Basic elements of Bohmian mechanics Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview 8. Interference effects in psychology - an introduction 9. A quantum-like model of decision making Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis 11. Bohmian mechanics in finance and economics 12. The Bohm-Vigier Model and path simulation 13. Other applications to economic/financial theory 14. The neurophysiological sources of quantum-like processing in the brain Conclusion Glossary Index.

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Quantum Social Science

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Journal of Physics B: atomic, molecular and optical physics

Electron–molecule collision calculations using the R-matrix method

To lay a foundation for the study and use of rotation operators in graduate quantum mechanics and in research, a thorough discussion is presented of rotations in Euclidean three space (R3 ) and of their effect on kets in the Hilbert space of a single particle. The Wigner D-matrices are obtained and used to rotate spherical harmonics. An extensive ready-reference appendix of the properties of these matrices, expressed in a consistent notation, is provided. Careful attention is paid throughout to various conventions (e.g. active versus passive viewpoints) that are used in the literature.

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A guide to rotations in quantum mechanics

Publisher Summary This chapter discusses the scattering of the near-threshold electron-molecule. Low-energy electron-molecule scattering is rich in fundamental physics and a fascinating phenomenon. It is a field whose applications range from pollution control to astrophysics. At energies near zero for elastic scattering and a few meV above threshold for inelastic processes, the calculation, understanding, and measurement of cross sections encounter unique challenges and bizarre phenomena. Frame transformations are an invaluable conceptual tool. But the few existing applications of this procedure bring into question their practical utility. Use of frame transformations in day-to-day scattering calculations, indeed seem feasible only if there exists a wide, energy-independent band of radii at which the transformation leads to accurate cross sections. In any case, strong sensitivity of the approximate cross sections to the transformation radii poses a serious problem. The body-frame fixed-nuclei (BF-FN) approximation can be considered a composite of the FNO and RR approximations in the BODY representation.

Near-Threshold Electron-Molecule Scattering

A joint experimental-theoretical attack on low-energy e-H2 scattering is described. The cross sections calculated from a highly converged numerical solution of the nonrelativistic Schrodinger equation, using a parameter-free interaction potential, are first compared with results from swarm experiments, and are later used to improve the accuracy of the swarm analysis at energies above the first vibrational threshold. To provide further perspective, the theoretical results are compared with a variety of other experimental data. The theoretical results for the momentum-transfer and rotational-excitation cross sections are in excellent agreement with the results from swarm experiments, but there is an unresolved and significant difference in the threshold behaviour of the vibrational-excitation cross sections. Both the theoretical and experimental approaches are subjected to close scrutiny in an attempt to uncover possible sources of error that could explain this difference. The failure to locate likely sources points to the need for further independent theoretical and experimental work to resolve a problem that has serious implications.

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Near-threshold rotational and vibrational excitation of H 2 by electron impact: Theory and experiment

Quantum States of Atoms, Molecules and Solids

The essential physical features of low-energy electron-molecule scattering are described in a qualitative fashion. The context for this discussion is provided by the frame-transformation picture, which entails a 'partitioning' of the quantum scattering problem according to the relative importance of various physical interactions. This picture is then used as the basis for a qualitative overview of several contemporary theoretical techniques for solving the quantum scattering problem that are based on eigenfunction expansions of the system wavefunction and for representing the electronmolecule interaction potential. Finally, progress in three specific problem areas of recent interest is surveyed. The emphasis throughout is on non-resonant elastic scattering and ro-vibrational excitation.

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Michael A. Morrison

Papers

A guide to rotations in quantum mechanics

Near-Threshold Electron-Molecule Scattering

Near-threshold rotational and vibrational excitation of H 2 by electron impact: Theory and experiment

Quantum States of Atoms, Molecules and Solids

The Physics of Low-energy Electron-Molecule Collisions: A Guide for the Perplexed and the Uninitiated